高等数学数据分析英文试题GMAT题库 (3)
Simple Linear Regression 393 CHAPTER 12: SIMPLE LINEAR REGRESSION
1.The Y-intercept (b0) represents the
a)predicted value of Y when X = 0.
b)change in estimated average Y per unit change in X.
c)predicted value of Y.
d)variation around the sample regression line.
ANSWER:
a
TYPE: MC DIFFICULTY: Easy
KEYWORDS: intercept, interpretation
2.The Y-intercept (b0) represents the
a)estimated average Y when X = 0.
b)change in estimated average Y per unit change in X.
c)predicted value of Y.
d)variation around the sample regression line.
ANSWER:
a
TYPE: MC DIFFICULTY: Easy
KEYWORDS: intercept, interpretation
3.The slope (b1) represents
a)predicted value of Y when X = 0.
b)the estimated average change in Y per unit change in X.
c)the predicted value of Y.
d)variation around the line of regression.
ANSWER:
b
TYPE: MC DIFFICULTY: Easy
KEYWORDS: slope, interpretation
4.The least squares method minimizes which of the following?
a)SSR
b)SSE
c)SST
d)All of the above
ANSWER:
b
TYPE: MC DIFFICULTY: Difficult
KEYWORDS: least squares, properties
394 Simple Linear Regression
TABLE 12-1
A large national bank charges local companies for using their services. A bank official reported the results of a regression analysis designed to predict the bank’s charges (Y ) -- measured in dollars per month -- for services rendered to local companies. One independent variable used to predict service charge to a company is the company’s sales revenue (X ) -- measured in millions of dollars. Data for 21 companies who use the bank’s services were used to fit the model:
E (Y )=β0+β1X
The results of the simple linear regression are provided below.
2,70020, 65, two-tailed value 0.034 (for testing )YX Y X S p β1
=?+==
5. Referring to Table 12-1, interpret the estimate of β0, the Y -intercept of the line. a) All companies will be charged at least $2,700 by the bank.
b) There is no practical interpretation since a sales revenue of $0 is a nonsensical value. c) About 95% of the observed service charges fall within $2,700 of the least squares line. d) For every $1 million increase in sales revenue, we expect a service charge to decrease
$2,700.
ANSWER: b
TYPE: MC DIFFICULTY: Moderate KEYWORDS: intercept, interpretation
6. Referring to Table 12-1, interpret the estimate of σ, the standard deviation of the random error
term (standard error of the estimate) in the model.
a) About 95% of the observed service charges fall within $65 of the least squares line. b) About 95% of the observed service charges equal their corresponding predicted values. c) About 95% of the observed service charges fall within $130 of the least squares line.
d) For every $1 million increase in sales revenue, we expect a service charge to increase $65.
ANSWER: c
TYPE: MC DIFFICULTY: Difficult
KEYWORDS: standard error of the estimate, interpretation
7. Referring to Table 12-1, interpret the p -value for testing whether β1 exceeds 0.
a) There is sufficient evidence (at the α = 0.05) to conclude that sales revenue (X ) is a
useful linear predictor of service charge (Y ).
b) There is insufficient evidence (at the α = 0.10) to conclude that sales revenue (X ) is a
useful linear predictor of service charge (Y ).
c) Sales revenue (X ) is a poor predictor of service charge (Y ).
d) For every $1 million increase in sales revenue, we expect a service charge to increase
$0.034.
ANSWER: a
TYPE: MC DIFFICULTY: Moderate KEYWORDS: p -value, interpretation
8. Referring to Table 12-1, a 95% confidence interval for β1 is (15, 30). Interpret the interval.
Simple Linear Regression 395
a)We are 95% confident that the mean service charge will fall between $15 and $30 per
month.
b)We are 95% confident that the sales revenue (X) will increase between $15 and $30
million for every $1 increase in service charge (Y).
c)We are 95% confident that average service charge (Y) will increase between $15 and $30
for every $1 million increase in sales revenue (X).
d)At the α = 0.05 level, there is no evidence of a linear relationship between service
charge (Y) and sales revenue (X).
ANSWER:
c
TYPE: MC DIFFICULTY: Moderate
KEYWORDS: confidence interval, interpretation
TABLE 12-2
A candy bar manufacturer is interested in trying to estimate how sales are influenced by the price of
their product. To do this, the company randomly chooses 6 small cities and offers the candy bar at different prices. Using candy bar sales as the dependent variable, the company will conduct a simple linear regression on the data below:
City Price ($) Sales
Falls 1.30 100
River
Hudson 1.60 90
Ellsworth 1.80 90
Prescott 2.00 40
Elm 2.40 38
Rock
Stillwater 2.90 32
9.Referring to Table 12-2, what is the estimated slope parameter for the candy bar price and sales
data?
a)161.386
b)0.784
c)– 3.810
d)– 48.193
ANSWER:
d
TYPE: MC DIFFICULTY: Moderate
KEYWORDS: slope, estimation
10.Referring to Table 12-2, what is the estimated average change in the sales of the candy bar if
price goes up by $1.00?
a)161.386
b)0.784
c)– 3.810
d)– 48.193
ANSWER:
d
TYPE: MC DIFFICULTY: Moderate
KEYWORDS: slope, interpretation
11.Referring to Table 12-2, what is the coefficient of correlation for these data?
396 Simple Linear Regression
a) – 0.8854 b) – 0.7839 c) 0.7839 d) 0.8854
ANSWER: a
TYPE: MC DIFFICULTY: Moderate
KEYWORDS: coefficient of correlation, estimation
12. Referring to Table 12-2, what is the percentage of the total variation in candy bar sales explained
by the regression model?
a) 100% b) 88.54% c) 78.39% d) 48.19%
ANSWER: c
TYPE: MC DIFFICULTY: Moderate
KEYWORDS: coefficient of determination, interpretation
13. Referring to Table 12-2, what percentage of the total variation in candy bar sales is explained by
prices?
a) 100% b) 88.54% c) 78.39% d) 48.19%
ANSWER: c
TYPE: MC DIFFICULTY: Moderate
KEYWORDS: coefficient of determination, interpretation
14. Referring to Table 12-2, what is the standard error of the estimate, S YX , for the data?
a) 0.784 b) 0.885 c) 12.650 d) 16.299
ANSWER: d
TYPE: MC DIFFICULTY: Moderate
KEYWORDS: standard error of the estimate, estimation
15. Referring to Table 12-2, what is the standard error of the regression slope estimate, ?
1b S
Simple Linear Regression 397
a)0.784
b)0.885
c)12.650
d)16.299
ANSWER:
c
TYPE: MC DIFFICULTY: Moderate
KEYWORDS: standard error, slope
16.Referring to Table 12-2, what is ∑(X–X 2 for these data?
a)0
b) 1.66
c) 2.54
d)25.66
ANSWER:
b
TYPE: MC DIFFICULTY: Moderate
KEYWORDS: sum of squares
17.Referring to Table 12-2, to test that the regression coefficient, β1, is not equal to 0, what would
be the critical values? Use α = 0.05.
±
a) 2.5706
±
b) 2.7764
±
c) 3.1634
±
d) 3.4954
ANSWER:
b
TYPE: MC DIFFICULTY: Difficult
KEYWORDS: t test on slope, critical value
18.Referring to Table 12-2, to test whether a change in price will have any impact on average sales,
what would be the critical values? Use α = 0.05.
±
a) 2.5706
±
b) 2.7765
±
c) 3.1634
±
d) 3.4954
ANSWER:
b
TYPE: MC DIFFICULTY: Difficult
EXPLANATION: This is a test for β1 is not equal to 0.
KEYWORDS: t test on slope, critical value
19.Referring to Table 12-2, if the price of the candy bar is set at $2, the estimated average sales will
be
398 Simple Linear Regression
a)30
b)65
c)90
d)100
ANSWER:
b
TYPE: MC DIFFICULTY: Moderate
KEYWORDS: estimation of mean values
20.Referring to Table 12-2, if the price of the candy bar is set at $2, the predicted sales will be
a)30
b)65
c)90
d)100
ANSWER:
b
TYPE: MC DIFFICULTY: Moderate
KEYWORDS: prediction of individual values
21.True of False: The Chancellor of a university has commissioned a team to collect data on
students’ GPAs and the amount of time they spend bar hopping every week (measured in
minutes). He wants to know if imposing much tougher regulations on all campus bars to make it more difficult for students to spend time in any campus bar will have a significant impact on
general students' GPAs. His team should use a t test on the slope of the population regression.
ANSWER:
True
TYPE: TF DIFFICULTY: Moderate
KEYWORDS: t test on slope
22.The residual represents the discrepancy between the observed dependent variable and its
_______ value.
ANSWER:
predicted or estimated average
TYPE: FI DIFFICULTY: Moderate
KEYWORDS: estimation of mean values, prediction of individual values
TABLE 12-3
Simple Linear Regression 399 The director of cooperative education at a state college wants to examine the effect of cooperative education job experience on marketability in the work place. She takes a random sample of 4 students. For these 4, she finds out how many times each had a cooperative education job and how many job offers they received upon graduation. These data are presented in the table below.
JobOffer
Student CoopJobs
4
1 1
2 2
6
3
3 1
1
4 0
23.Referring to Table 12-3, set up a scatter diagram.
ANSWER:
KEYWORDS: scatter plot
24.Referring to Table 12-3, the least squares estimate of the slope is __________.
ANSWER:
2.50
TYPE: FI DIFFICULTY: 2 Moderate
KEYWORDS: slope, estimation, least squares
25.Referring to Table 12-3, the least squares estimate of the Y-intercept is __________.
ANSWER:
1.00
TYPE: FI DIFFICULTY: Moderate
KEYWORDS: intercept, estimation, least squares
26.Referring to Table 12-3, the prediction for the number of job offers for a person with 2 coop jobs
is __________.
400 Simple Linear Regression
ANSWER:
6
TYPE: FI DIFFICULTY: Moderate
KEYWORDS: prediction of individual values
27.Referring to Table 12-3, the total sum of squares (SST) is __________.
ANSWER:
13.0
TYPE: FI DIFFICULTY: Moderate
KEYWORDS: sum of squares
28.Referring to Table 12-3, the regression sum of squares (SSR) is __________.
ANSWER:
12.5
TYPE: FI DIFFICULTY: Moderate
KEYWORDS: sum of squares
29.Referring to Table 12-3, the error or residual sum of squares (SSE) is __________.
ANSWER:
0.50
TYPE: FI DIFFICULTY: Moderate
KEYWORDS: sum of squares
30.Referring to Table 12-3, the coefficient of determination is __________.
ANSWER:
0.962
TYPE: FI DIFFICULTY: Moderate
KEYWORDS: coefficient of determination
31. Referring to Table 12-3, the standard error of estimate is __________.
ANSWER:
0.50
TYPE: FI DIFFICULTY: Moderate
KEYWORDS: standard error of estimate
32.Referring to Table 12-3, the coefficient of correlation is __________.
ANSWER:
0.981
TYPE: FI DIFFICULTY: Moderate
KEYWORDS: coefficient of correlation
33.Referring to Table 12-3, suppose the director of cooperative education wants to obtain a 95%
confidence-interval estimate for the mean number of job offers received by people who have had exactly one cooperative education job. The t critical value she would use is ________.
Simple Linear Regression 401 ANSWER:
4.3027
TYPE: FI DIFFICULTY: Easy
KEYWORDS: confidence interval, estimation of mean values, critical value
34.Referring to Table 12-3, suppose the director of cooperative education wants to obtain a 95%
confidence interval estimate for the mean number of job offers received by people who have had exactly one cooperative education job. The confidence interval is from ________ to ________. ANSWER:
2.424 to 4.576
TYPE: FI DIFFICULTY: Moderate
KEYWORDS: confidence interval, estimation of mean values, critical value
35.Referring to Table 12-3, suppose the director of cooperative education wants to obtain a 95%
prediction interval estimate for the number of job offers received by people who have had exactly one cooperative education job. The prediction interval is from ________ to ________. ANSWER:
1.0947 to 5.9053
TYPE: FI DIFFICULTY: Moderate
KEYWORDS: prediction interval, prediction of individual values
36.True or False: Referring to Table 12-3, suppose the director of cooperative education wants to
obtain two 95% confidence interval estimates. One is for the mean number of job offers received by people who have had exactly one cooperative education job and one for people who have had two. The confidence interval for people who have had one cooperative education job would be the wider of the two intervals.
ANSWER:
False
TYPE: TF DIFFICULTY: Moderate
KEYWORDS: confidence interval, estimation of mean values
37.Referring to Table 12-3, suppose the director of cooperative education wants to obtain a 95%
prediction interval for the number of job offers received by a person who has had exactly two cooperative education jobs. The t critical value she would use is ________.
ANSWER:
4.3027
TYPE: FI DIFFICULTY: Moderate
KEYWORDS: prediction interval, prediction of individual values, critical value
38.Referring to Table 12-3, suppose the director of cooperative education wants to obtain a 95%
prediction interval for the number of job offers received by a person who has had exactly two cooperative education jobs. The prediction interval is from ________ to ________. ANSWER:
3.154 to 8.846
402 Simple Linear Regression
TYPE: FI DIFFICULTY: Moderate
KEYWORDS: prediction interval, prediction of individual values
39.True or False: Referring to Table 12-3, suppose the director of cooperative education wants to
obtain both a 95% confidence interval estimate and a 95% prediction interval for X = 2. The
confidence interval estimate would be the wider of the two intervals.
ANSWER:
False
TYPE: TF DIFFICULTY: Moderate
KEYWORDS: confidence interval, prediction interval, estimation of mean values, prediction of individual values, properties
40.Referring to Table 12-3, the director of cooperative education wanted to test the hypothesis that
the true slope was equal to 0. The denominator of the test statistic is s. The value of s in this
b1b1 sample is ________.
ANSWER:
0.3536
TYPE: FI DIFFICULTY: Moderate
KEYWORDS: t test on slope, standard error, slope
41.Referring to Table 12-3, the director of cooperative education wanted to test the hypothesis that
the true slope was equal to 0. The value of the test statistic is ________.
ANSWER:
7.07
TYPE: FI DIFFICULTY: Moderate
KEYWORDS: t test on slope, test statistic, slope
42.Referring to Table 12-3, the director of cooperative education wanted to test the hypothesis that
the true slope was equal to 3.0. The value of the test statistic is ________.
ANSWER:
-1.4142
TYPE: FI DIFFICULTY: Moderate
KEYWORDS: t test on slope, test statistic, slope
43.Referring to Table 12-3, the director of cooperative education wanted to test the hypothesis that
the true slope was equal to 0. For a test with a level of significance of 0.05, the null hypothesis should be rejected if the value of the test statistic is ________.
ANSWER:
> 4.3027 or < -4.3027
TYPE: FI DIFFICULTY: Easy
KEYWORDS: t test on slope, critical value, slope, decision
Simple Linear Regression 403
44. Referring to Table 12-3, the director of cooperative education wanted to test the hypothesis that
the true slope was equal to 3.0. For a test with a level of significance of 0.05, the null hypothesis should be rejected if the value of the test statistic is ________.
ANSWER:
> 4.3027 or < -4.3027
TYPE: FI DIFFICULTY: Easy
KEYWORDS: t test on slope, critical value, slope, decision
45. Referring to Table 12-3, the director of cooperative education wanted to test the hypothesis that
the true slope was equal to 0. The p -value of the test is between ________ and ________.
ANSWER:
0.01 and 0.02 using the Table, or 0.0194 using Excel TYPE: FI DIFFICULTY: Moderate
KEYWORDS: t test on slope, p -value, slope
46. Referring to Table 12-3, the director of cooperative education wanted to test the hypothesis that
the true slope was equal to 3.0. The p -value of the test is between ________ and ________.
ANSWER:
0.2 and 0.5 using the Table, or 0.2929 using Excel TYPE: FI DIFFICULTY: Difficult EXPLANATION: The t-test statistic is ()()1
11 2.53 1.41420.3536
b b t S β??=
==?
KEYWORDS: t test on slope, p -value, slope
TABLE 12-4
The managers of a brokerage firm are interested in finding out if the number of new clients a broker brings into the firm affects the sales generated by the broker. They sample 12 brokers and determine the number of new clients they have enrolled in the last year and their sales amounts in thousands of dollars. These data are presented in the table that follows.
Broker Clients Sales 1 27 52
404 Simple Linear Regression
2 11 37
3 42 64
4 33 55
5 15 29
6 15 34
7 25 58
8 36 59
9 28 44
10 30 48
11 17 31
12 22 38
47.Referring to Table 12-4, set up a scatter diagram.
KEYWORDS: scatter plot
48.Referring to Table 12-4, the least squares estimate of the slope is __________.
ANSWER:
1.12
TYPE: FI DIFFICULTY: Moderate
KEYWORDS: slope, estimation, least squares
49.Referring to Table 12-4, the least squares estimate of the Y-intercept is __________.
Simple Linear Regression 405 ANSWER:
17.7
TYPE: FI DIFFICULTY: Moderate
KEYWORDS: intercept, estimation, least squares
50.Referring to Table 12-4, the prediction for the amount of sales (in $1,000s) for a person who
brings 25 new clients into the firm is ________.
ANSWER:
45.66
TYPE: FI DIFFICULTY: Moderate
KEYWORDS: prediction of individual values
51.Referring to Table 12-4, the total sum of squares (SST) is __________.
ANSWER:
1,564.2
TYPE: FI DIFFICULTY: Moderate
KEYWORDS: sum of squares
52.Referring to Table 12-4, the regression sum of squares (SSR) is __________.
ANSWER:
1,227.4
TYPE: FI DIFFICULTY: Moderate
KEYWORDS: sum of squares
53.Referring to Table 12-4, the error or residual sum of squares (SSE) is __________. ANSWER:
336.9
TYPE: FI DIFFICULTY: Moderate
KEYWORDS: sum of squares
54.Referring to Table 12-4, the coefficient of determination is __________.
ANSWER:
0.785
TYPE: FI DIFFICULTY: Moderate
KEYWORDS: coefficient of determination
55.Referring to Table 12-4, ______% of the total variation in sales generated can be explained by the
number of new clients brought in.
ANSWER:
78.5
TYPE: FI DIFFICULTY: Moderate
KEYWORDS: coefficient of determination, interpretation
56.Referring to Table 12-4, the standard error of the estimated slope coefficient is __________.
406 Simple Linear Regression
ANSWER:
0.185
TYPE: FI DIFFICULTY: Moderate
KEYWORDS: slope, standard error
57.Referring to Table 12-4, the standard error of estimate is __________.
ANSWER:
5.804
TYPE: FI DIFFICULTY: Moderate
KEYWORDS: standard error of estimate
58.Referring to Table 12-4, the coefficient of correlation is __________.
ANSWER:
0.886
TYPE: FI DIFFICULTY: Moderate
KEYWORDS: coefficient of correlation
59.Referring to Table 12-4, suppose the managers of the brokerage firm want to obtain a 99%
confidence interval estimate for the mean sales made by brokers who have brought into the firm
24 new clients. The t critical value they would use is ________.
ANSWER:
3.1693
TYPE: FI DIFFICULTY: Easy
KEYWORDS: estimation of mean values, confidence interval, critical value
60.Referring to Table 12-4, suppose the managers of the brokerage firm want to obtain a 99%
confidence interval estimate for the mean sales made by brokers who have brought into the firm
24 new clients. The confidence interval is from ________ to ________.
ANSWER:
39.19 to 49.89
TYPE: FI DIFFICULTY: Moderate
KEYWORDS: estimation of mean values, confidence interval
61.Referring to Table 12-4, suppose the managers of the brokerage firm want to obtain a 99%
prediction interval for the sales made by a broker who has brought into the firm 18 new clients.
The t critical value they would use is ________.
ANSWER:
3.1693
TYPE: FI DIFFICULTY: Moderate
KEYWORDS: prediction of individual values, prediction interval, critical value
Simple Linear Regression 407 62.Referring to Table 12-4, suppose the managers of the brokerage firm want to obtain a 99%
prediction interval for the sales made by a broker who has brought into the firm 18 new clients.
The prediction interval is from ________ to ________.
ANSWER:
18.23 to 57.42
TYPE: FI DIFFICULTY: Moderate
KEYWORDS: prediction of individual values, prediction interval
63.Referring to Table 12-4, suppose the managers of the brokerage firm want to obtain both a 99%
confidence interval estimate and a 99% prediction interval for X = 24. The confidence interval estimate would be the __________ (wider or narrower) of the two intervals.
ANSWER:
narrower
TYPE: FI DIFFICULTY: Moderate
KEYWORDS: prediction of individual values, prediction interval, estimation of mean values, confidence interval, properties
64.Referring to Table 12-4, the managers of the brokerage firm wanted to test the hypothesis that the
true slope was equal to 0. The denominator of the test statistic is s. The value of s in this
b1b1 sample is ________.
ANSWER:
0.1853
TYPE: FI DIFFICULTY: Moderate
KEYWORDS: t test on slope, slope, standard error
65.Referring to Table 12-4, the managers of the brokerage firm wanted to test the hypothesis that the
true slope was equal to 0. The value of the test statistic is _______.
ANSWER:
6.04
TYPE: FI DIFFICULTY: Moderate
KEYWORDS: t test on slope, slope, test statistic
66.Referring to Table 12-4, the managers of the brokerage firm wanted to test the hypothesis that the
number of new clients brought in did not affect the amount of sales generated. The value of the test statistic is _______.
ANSWER:
6.04
TYPE: FI DIFFICULTY: Moderate
KEYWORDS: t test on slope, slope, test statistic
408 Simple Linear Regression
67.Referring to Table 12-4, the managers of the brokerage firm wanted to test the hypothesis that the
true slope was equal to 0. For a test with a level of significance of 0.01, the null hypothesis
should be rejected if the value of the test statistic is ________.
ANSWER:
> 3.1693 or < -3.1693
TYPE: FI DIFFICULTY: Moderate
KEYWORDS: t test on slope, slope, critical value, decision
68.Referring to Table 12-4, the managers of the brokerage firm wanted to test the hypothesis that the
true slope was equal to 0. The p-value of the test is ________.
ANSWER:
< 0.01 using the Table, or 0.000126 using Excel
TYPE: FI DIFFICULTY: Moderate
KEYWORDS: t test on slope, slope, p-value
69.Referring to Table 12-4, the managers of the brokerage firm wanted to test the hypothesis that the
true slope was equal to 0. At a level of significance of 0.01, the null hypothesis should be
_______ (accepted or rejected).
ANSWER:
rejected
TYPE: FI DIFFICULTY: Moderate
KEYWORDS: t test on slope, slope, decision
70.Referring to Table 12-4, the managers of the brokerage firm wanted to test the hypothesis that the
true slope was equal to 0. At a level of significance of 0.01, the decision that should be made
implies that _____ (there is or there is no) linear dependent relation between the independent
and dependent variables.
ANSWER:
there is
TYPE: FI DIFFICULTY: Moderate
KEYWORDS: t test on slope, slope, conclusion
71.Referring to Table 12-4, the managers of the brokerage firm wanted to test the hypothesis that the
number of new clients brought in had a positive impact on the amount of sales generated. The
value of the test statistic is _______.
ANSWER:
6.04
TYPE: FI DIFFICULTY: Moderate
KEYWORDS: t test on slope, slope, test statistic
72.Referring to Table 12-4, the managers of the brokerage firm wanted to test the hypothesis that the
number of new clients brought in had a positive impact on the amount of sales generated. For a
Simple Linear Regression 409 test with a level of significance of 0.01, the null hypothesis should be rejected if the value of the test statistic is ________.
ANSWER:
> 2.7638
TYPE: FI DIFFICULTY: Moderate
KEYWORDS: t test on slope, slope, critical value, decision
73.Referring to Table 12-4, the managers of the brokerage firm wanted to test the hypothesis that the
number of new clients brought in had a positive impact on the amount of sales generated. The p-value of the test is ________.
ANSWER:
< 0.005 using the Table, or 0.000126/2 using Excel
TYPE: FI DIFFICULTY: Moderate
KEYWORDS: t test on slope, slope, p-value
74.Referring to Table 12-4, the managers of the brokerage firm wanted to test the hypothesis that the
number of new clients brought in had a positive impact on the amount of sales generated. At a level of significance of 0.01, the null hypothesis should be _______ (accepted or rejected). ANSWER:
rejected
TYPE: FI DIFFICULTY: Moderate
KEYWORDS: t test on slope, slope, decision
75.Referring to Table 12-4, the managers of the brokerage firm wanted to test the hypothesis that the
number of new clients brought in had a positive impact on the amount of sales generated. At a level of significance of 0.01, the decision that should be made implies that the number of new clients brought in _____ (had or did not have) a positive impact on the amount of sales
generated.
ANSWER:
had
TYPE: FI DIFFICULTY: Moderate
KEYWORDS: t test on slope, slope, conclusion
TABLE 12-5
The managing partner of an advertising agency believes that his company's sales are related to the industry sales. He uses Microsoft Excel’s Data Analysis tool to analyze the last 4 years of quarterly data (i.e., n = 16) with the following results:
Regression Statistics
Multiple R 0.802
R Square 0.643
Adjusted R Square 0.618
Standard Error SYX 0.9224
410 Simple Linear Regression
16 Observations
ANOVA df SS MS F Sig.F R 1.27 0.000egression 21.497 21.497 25 Error 14 11.912 0.851 Total 15 33.409
Predictor Coef StdError t Stat P-value Intercept 3.962 1.440 2.75 0.016 Industry 0.040451 0.008048 5.03 0.000
Durbin-Watson Statistic 1.59
76. Referring to Table 12-5, the value of the quantity that the least squares regression line minimizes
ANSWER: IFFICULTY: Moderate
s, sum of squares
ANSWER:
040451
TY: Easy
imation
for a quarter in which X = 120 is Y = ________. IFFICULTY: Moderate
values 9. Referring to Table 12-5, the standard error of the estimate is ________.
IFFICULTY: Easy
timate
ination is ________. is ________.
11.912
FI D TYPE: KEYWORDS: least squares, propertie 77. Referring to Table 12-5, the estimates of the Y -intercept and slope are ________ and ________,
respectively.
3.962 and 0.TYPE: FI DIFFICUL KEYWORDS: intercept, slope, est 78. Referring to Table 12-5, the prediction
ANSWER: 8.816
: FI D TYPE KEYWORDS: prediction of individual
7ANSWER: 0.9224
I D TYPE: F KEYWORDS: standard error of es 80. Referring to Table 12-5, the coefficient of determ
ANSWER: 0.643
Simple Linear Regression 411
FI DIFFICULTY: Easy
mination
81. Referring to Table 12-5, the standard error of the estimated slope coefficient is ________.
ANSWER: FI DIFFICULTY: Easy r
82. Referring to Table 12-5, the correlation coefficient is ________.
ANSWER: FI DIFFICULTY: Easy
lation
83. Referring to Table 12-5, the partner wants to test for autocorrelation using the Durbin-Watson
ANSWER: IFFICULTY: Easy
tistic, critical value, autocorrelation
84. Referring to Table 12-5, the partner wants to test for autocorrelation using the Durbin-Watson
onclusion. rm the test.
ANSWER: PE: MC DIFFICULTY: Moderate
decision, autocorrelation 5. If the Durbin-Watson statistic has a value close to 0, which assumption is violated?
NSWER: PE: MC Difficulty: Easy
n statistic, autocorrelation, assumption TYPE:KEYWORDS: coefficient of deter 0.008
TYPE:KEYWORDS: slope, standard erro 0.802
TYPE: KEYWORDS: coefficient of corre statistic. Using a level of significance of 0.05, the critical values of the test are d L = ________, and d U = ________. 1.10; 1.37
TYPE: FI D KEYWORDS: Durbin-Watson sta statistic. Using a level of significance of 0.05, the decision he should make is:
a) there is evidence of autocorrelation.
b) the test is unable to make a definite c c) there is no evidence of autocorrelation.
d) there is not enough information to perfo c
TY KEYWORDS: Durbin-Watson statistic,
8a) Normality of the errors. b) Independence of errors. c) Homoscedasticity. d) None of the above.
A b
TY KEYWORDS: Durbin-Watso
412 Simple Linear Regression
6. If the Durbin-Watson statistic has a value close to 4, which assumption is violated?
NSWER: PE: MC Difficulty: Easy
n statistic, assumption, autocorrelation 7. The standard error of the estimate is a measure of
egression line. variable.
ANSWER: PE: MC DIFFICULTY: Easy
mate, interpretation
88. The coefficient of determination (r ) tells us
s larger than 1. otal variation. .
ANSWER: PE: MC DIFFICULTY: Easy
ination, interpretation
ABLE 12-6
The following EXCEL tables are obtained when "Score received on an exam (measured in percentage
Regression Statistics
8a) Normality of the errors. b) Independence of errors. c) Homoscedasticity. d) None of the above.
A b
TY KEYWORDS: Durbin-Watso
8a) total variation of the Y variable.
b) the variation around the sample r c) explained variation.
d) the variation of the X b
TY KEYWORDS: standard error of esti 2a) that the coefficient of correlation (r ) i b) whether r has any significance.
c) that we should not partition the t d) the proportion of total variation that is explained d
TY KEYWORDS: coefficient of determ
T points)" (Y) is regressed on "percentage attendance" (X) for 22 students in a Statistics for Business and Economics course. Multiple 620229 R 0.142R Square 0.02034053 Adjusted R Square -0.028642444 Standard Error 20.25979924
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高等数学试题及答案文件排版存档编号：[UYTR-OUPT28-KBNTL98-UYNN208]
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高等数学上考试试题及答案
四川理工学院试卷（2007至2008学年第一学期） 课程名称： 高等数学(上)(A 卷) 命题教师： 杨 勇 适用班级： 理工科本科 考试(考查)： 考试 2008年 1 月 10日 共 6 页 注意事项： 1、 满分100分。要求卷面整洁、字迹工整、无错别字。 2、 考生必须将姓名、班级、学号完整、准确、清楚地填写在试卷规定的地方，否 则视为废卷。 3、 考生必须在签到单上签到，若出现遗漏，后果自负。 4、 如有答题纸，答案请全部写在答题纸上，否则不给分；考完请将试卷和答题卷 分别一同交回，否则不给分。 试 题 一、单选题（请将正确的答案填在对应括号内，每题3分，共15分） 1. =--→1 ) 1sin(lim 21x x x ( C ) (A) 1； (B) 0； (C) 2； (D) 2 1 2.若)(x f 的一个原函数为)(x F ，则dx e f e x x )(? --为( B ) (A) c e F x +)(； (B) c e F x +--)(； (C) c e F x +-)(； (D ) c x e F x +-) ( 3.下列广义积分中 ( D )是收敛的. (A) ? +∞ ∞ -xdx sin ； (B)dx x ? -111 ； (C) dx x x ?+∞ ∞-+2 1； (D)?∞-0dx e x 。 4. )(x f 为定义在[]b a ,上的函数，则下列结论错误的是( B )
(A) )(x f 可导，则)(x f 一定连续； (B) )(x f 可微，则)(x f 不一定可导； (C) )(x f 可积（常义），则)(x f 一定有界； (D) 函数)(x f 连续，则? x a dt t f )(在[]b a ,上一定可导。 5. 设函数=)(x f n n x x 211lim ++∞→ ，则下列结论正确的为( D ) (A) 不存在间断点； (B) 存在间断点1=x ； (C) 存在间断点0=x ； (D) 存在间断点1-=x 二、填空题（请将正确的结果填在横线上.每题3分，共18分） 1. 极限=-+→x x x 1 1lim 20 _0____. 2. 曲线? ??=+=3 2 1t y t x 在2=t 处的切线方程为______. 3. 已知方程x xe y y y 265=+'-''的一个特解为x e x x 22 )2(2 1+- ，则该方程的通解为 . 4. 设)(x f 在2=x 处连续，且22 ) (lim 2=-→x x f x ，则_____)2(='f 5．由实验知道，弹簧在拉伸过程中需要的力F （牛顿）与伸长量s 成正比，即ks F =（k 为比例系数），当把弹簧由原长拉伸6cm 时，所作的功为_________焦耳。 6．曲线23 3 2 x y =上相应于x 从3到8的一段弧长为 . 三、设0→x 时，)(22 c bx ax e x ++-是比2 x 高阶的无穷小，求常数c b a ,,的值（6分）
高等数学试题库
高等数学试题库 第一章 极限与连续 一．判断题 1-1-1 函数y=1/ln(x+1)的定义域是(-1, ∞)．( ) 1-1-2 函数y=lg((1-x)/(1+x))是奇函数．( ) 1-1-3 函数y=x 2+1的反函数是y=(x+1)1/2．( ) 1-1-4 y=arctgx+1010是有界函数．( ) 1-1-5 若()lim x f x →=2 3，则f(2)=3．( ) 1-1-6 若()lim x f x →=23，则f(x)在x=2处连续．( ) 1-1-7 若f(x)在x 0无定义，则lim x x →0 f(x)必不存在．( ) 1-1-8 lim sin lim limsin x x x x x x x →→→=?=0100 10．( ) 1-1-9 lim x →1 (1/(1-x)－1/(1-x 3))= lim x →11/(1-x)－lim x →11/(1-x 3)=∞- ∞=0．( ) 1-1-10 lim x →1x/(x-1)= lim x →1x/lim x →1(x-1)= ∞．( ) 1-1-11 lim n →∞(1/n 2+2/n 2+3/n 2+…+n/n 2)=0+0+0+…+0=0．( ) 1-1-12 若f(x 0-0)=f(x 0+0)，则f(x)在x 0连续．( ) 1-1-13 方程x ·2x =1至少有一个小于1的正数根．( ) 1-1-14 若f(x)在闭区间[a ，b]上不连续，则f(x)在闭区间[a ，b]上必无最大值和最小 值．( ) 二．填空题 1-2-1 lim x →4 (x 2-5x+4)/(x-4)=________． 1-2-2 lim x x x →+--42134 =________． 1-2-3 lim n →∞ (1+2+3+…+n)/n 2=________． 1-2-4 lim x →0x 2/(1-cosx)=________． 1-2-5 lim n →∞ n[ln(1+n)-ln(n)]=________． 1-2-6 设f(x)= sin ,, x x x 222+≠=???ππ ，则lim x →πf(x)=________． 1-2-7 当a=________时，函数f(x)= a x x x x x x ++≤>???21030,sin , ，在x=0处连续． 1-2-8 函数 f(x)= (x-1)/(x 2+x-2) 的间断点是＿＿＿＿． 1-2-9 已知极限lim x →3 (x 2-2x+k)/(x-3) 存在(k 为实数)，则此极限值是________．
高等数学(下)练习题和答案
高等数学 一、填空 、选择题（每题3分，共30分） 1．曲面z xy =上点(1,2,2)处的法线方程为 . 2.已知D 是由直线1,1x y x y +=-=及0x =所围,则D yd σ=?? . 3.若曲线L 是2 2 1x y +=在第一象限的部分,则L xds =? . 4.设(,)ln()2y f x y x x =+ ,则(1,0)xx f = . 5.若级数 1 (2)n n u ∞ =+∑收敛,则lim n n u →∞ = . 6.函数3 2 2 (,)42f x y x x xy y =-+-,下列说法正确的是( ). (A)点(2,2)是(,)f x y 的极小值点; (B) 点(0,0)是(,)f x y 的极大值点; (C) 点(2,2)不是(,)f x y 的驻点; (D)(0,0)f 不是(,)f x y 的极值. 7.函数2 2 (,)f x y x y =+在点(1,1)处沿着那个方向的方向导数最大?( ) (A) (1,1); (B) (2,2); (C) (0,1); (D) (1,0). 8.曲线L 为沿2 24x y +=顺时针一周,则 1 2 L xdy ydx -=??( ). (A)2π- (B) 4π; (C) 4π-; (D)0. 9. 累次积分1 (,)y dy f x y dx ? 改变积分次序后等于( ). (A) 2 1 0(,)x x dx f x y dy ? ? ; (B) 21 (,)x x dx f x y dy ? ?; (C) 1 (,)x dx f x y dy ? ; (D) 21 (,)x dx f x y dy ?. 10. 下列各级数中条件收敛的是（ ） (A) 1 1 (1) n n ∞ +=-∑; (B) 1 2 11 (1)n n n ∞ +=-∑; (C) 1 1 (1) 1 n n n n ∞ +=-+∑; (D) 1 1 1 (1)(1) n n n n ∞ +=-+∑; 二解答题(6*4) 1.设函数22 ln()y x z x y e =++,求(1,0) dz . 2.设sin ,,2u z e v u xy v x y ===-,求 ,z z x y ????.
(完整)高等数学练习题(附答案)
《高等数学》 专业 年级 学号 姓名 一、判断题. 将√或×填入相应的括号内.（每题2分，共20分） （ ）1. 收敛的数列必有界. （ ）2. 无穷大量与有界量之积是无穷大量. （ ）3. 闭区间上的间断函数必无界. （ ）4. 单调函数的导函数也是单调函数. （ ）5. 若)(x f 在0x 点可导，则)(x f 也在0x 点可导. （ ）6. 若连续函数)(x f y =在0x 点不可导，则曲线)(x f y =在))(,(00x f x 点没有切线. （ ）7. 若)(x f 在[b a ,]上可积，则)(x f 在[b a ,]上连续. （ ）8. 若),(y x f z =在（00,y x ）处的两个一阶偏导数存在，则函数),(y x f z =在（00,y x ）处可微. （ ）9. 微分方程的含有任意常数的解是该微分方程的通解. （ ）10. 设偶函数)(x f 在区间)1,1(-内具有二阶导数，且 1)0()0(+'=''f f , 则 )0(f 为)(x f 的一个极小值. 二、填空题.（每题2分，共20分） 1. 设2 )1(x x f =-，则=+)1(x f . 2. 若1 212)(11+-= x x x f ，则=+→0 lim x . 3. 设单调可微函数)(x f 的反函数为)(x g , 6)3(,2)1(,3)1(=''='=f f f 则 =')3(g . 4. 设y x xy u + =, 则=du .
5. 曲线3 26y y x -=在)2,2(-点切线的斜率为 . 6. 设)(x f 为可导函数,)()1()(,1)1(2 x f x f x F f +==',则=')1(F . 7. 若 ),1(2)(0 2x x dt t x f +=? 则=)2(f . 8. x x x f 2)(+=在[0,4]上的最大值为 . 9. 广义积分 =-+∞? dx e x 20 . 10. 设D 为圆形区域=+≤+??dxdy x y y x D 5 2 2 1, 1 . 三、计算题（每题5分，共40分） 1. 计算)) 2(1 )1(11(lim 222n n n n ++++∞→Λ. 2. 求10 3 2 )10()3()2)(1(++++=x x x x y ΛΛ在（0，+∞）内的导数. 3. 求不定积分 dx x x ? -) 1(1. 4. 计算定积分 dx x x ? -π 53sin sin . 5. 求函数2 2 3 24),(y xy x x y x f -+-=的极值. 6. 设平面区域D 是由x y x y == ,围成，计算dxdy y y D ?? sin . 7. 计算由曲线x y x y xy xy 3,,2,1====围成的平面图形在第一象限的面积. 8. 求微分方程y x y y 2- ='的通解. 四、证明题（每题10分，共20分） 1. 证明：tan arc x = )(+∞<<-∞x .
高等数学试卷和答案新编
高等数学（下）模拟试卷一 一、填空题（每空3分，共15分） （1）函数 11z x y x y =+ +-的定义域为 （2）已知函数 arctan y z x =，则z x ?= ? （3）交换积分次序， 2 220 (,)y y dy f x y dx ? ? ＝ （4）已知L 是连接(0,1),(1,0)两点的直线段，则 ()L x y ds +=? （5）已知微分方程230y y y '''+-=，则其通解为 二、选择题（每空3分，共15分） （1）设直线L 为321021030x y z x y z +++=?? --+=?，平面π为4220x y z -+-=，则（） A.L 平行于πB.L 在π上C.L 垂直于πD.L 与π斜交 （2）设是由方程 222 2xyz x y z +++=确定，则在点(1,0,1)-处的dz =（） dx dy +2dx dy +22dx dy +2dx dy -（3）已知Ω是由曲面222425()z x y =+及平面5 z =所围成的闭区域，将 2 2()x y dv Ω +???在柱面坐标系下化成三次积分为（） 22 5 3 d r dr dz πθ? ??. 24 5 3 d r dr dz πθ? ?? 22 5 3 50 2r d r dr dz πθ? ??. 22 5 20 d r dr dz π θ? ?? （4）已知幂级数，则其收敛半径（） 2112 2（5）微分方程3232x y y y x e '''-+=-的特解y *的形式为y * =（） ()x ax b xe +()x ax b ce ++()x ax b cxe ++ 三、计算题（每题8分，共48分） 1、 求过直线1L :1231 01x y z ---==-且平行于直线2L ：21211x y z +-==的平面方程 2、 已知 22 (,)z f xy x y =，求z x ??，z y ?? 3、 设 22{(,)4}D x y x y =+≤，利用极坐标求 2 D x dxdy ?? 4、 求函数 22 (,)(2)x f x y e x y y =++的极值 得分 阅卷人
(完整版)高等数学试题及答案.doc
《高等数学》试题 30 考试日期： 2004 年 7 月 14 日 星期三 考试时间： 120 分钟 一. 选择题 1. 当 x 0 时， y ln(1 x) 与下列那个函数不是等价的 （ ） A) 、 y x B)、 y sin x C) 、 y 1 cos x D)、 y e x 1 2. 函数 f(x) 在点 x 0 极限存在是函数在该点连续的（ ） A 必要条件 B )、 充分条件 C )、 充要条件 D )、 无关条件 )、 3. 下列各组函数中， f (x) 和 g( x) 不是同一函数的原函数的有（ ） . A) 、 f ( x) 1 x e x 2 1 e x e x 2 2 e , g x 2 B)、 f (x) ln x a 2 x 2 , g x ln a 2 x 2 x C)、 f ( x) arcsin 2x 1 , g x 3 2arcsin 1 x D)、 f ( x) csc x sec x, g x tan x 2 4. 下列各式正确的是（ ） A ）、 x x dx 2x ln 2 C B ）、 sin tdt cost C C ）、 dx dx arctan x D ）、 ( 1 )dx 1 C 1 x 2 x 2 x 5. 下列等式不正确的是（ ） . A ）、 d b f x dx f x B ）、 d b x f x dt f b x b x a a dx dx d x f x dx f x D ）、 d x F x C ）、 a F t dt dx dx a x t) dt 6. lim ln(1 x （ ） x 0 A ）、0 B ）、 1 C ）、 2 D ）、 4 7. 设 f (x) sin bx ，则 xf ( x)dx （ ） A ）、 x cosbx sin bx C B ）、 x cosbx cosbx C b b C ）、 bxcosbx sinbx C D ）、 bxsin bx b cosbx C
(完整版)高等数学试题及答案
《高等数学》试题30 考试日期：2004年7月14日 星期三 考试时间：120 分钟 一.选择题 1. 当0→x 时，)1ln(x y +=与下列那个函数不是等价的 （ ） A)、x y = B)、x y sin = C)、x y cos 1-= D)、1-=x e y 2. 函数f(x)在点x 0极限存在是函数在该点连续的（ ） A )、必要条件 B )、充分条件 C )、充要条件 D )、无关条件 3. 下列各组函数中，)(x f 和)(x g 不是同一函数的原函数的有（ ）. A)、()()() 222 1 ,21)(x x x x e e x g e e x f ---=-= B) 、(( )) ()ln ,ln f x x g x x ==- C)、()()x x g x x f --=-=1arcsin 23,12arcsin )( D)、()2 tan ,sec csc )(x x g x x x f =+= 4. 下列各式正确的是（ ） A ）、2ln 2x x x dx C =+? B ）、sin cos tdt t C =-+? C ）、 2arctan 1dx dx x x =+? D ）、2 11 ()dx C x x -=-+? 5. 下列等式不正确的是（ ）. A ）、 ()()x f dx x f dx d b a =??????? B ）、()()()[]()x b x b f dt x f dx d x b a '=??????? C ）、()()x f dx x f dx d x a =??????? D ）、()()x F dt t F dx d x a '=???? ??'? 6. 0 ln(1)lim x x t dt x →+=?（ ） A ）、0 B ）、1 C ）、2 D ）、4 7. 设bx x f sin )(=，则=''?dx x f x )(（ ） A ）、 C bx bx b x +-sin cos B ） 、C bx bx b x +-cos cos C ）、C bx bx bx +-sin cos D ）、C bx b bx bx +-cos sin
大学高等数学上习题(附答案)
《高数》习题1（上） 一．选择题 1．下列各组函数中，是相同的函数的是（ ）. （A ）()()2ln 2ln f x x g x x == 和 （B ）()||f x x = 和 ( )g x =（C ）()f x x = 和 ( )2 g x = （D ）()|| x f x x = 和 ()g x =1 4．设函数()||f x x =，则函数在点0x =处（ ）. （A ）连续且可导 （B ）连续且可微 （C ）连续不可导 （D ）不连续不可微 7． 211 f dx x x ??' ???? 的结果是（ ）. （A ）1f C x ?? - + ??? （B ）1f C x ?? --+ ??? （C ）1f C x ?? + ??? （D ）1f C x ?? -+ ??? 10．设()f x 为连续函数，则()10 2f x dx '?等于（ ）. （A ）()()20f f - （B ）()()11102f f -????（C ）()()1 202f f -??? ?（D ）()()10f f - 二．填空题 1．设函数()21 00x e x f x x a x -?-≠? =??=? 在0x =处连续，则a = . 2．已知曲线()y f x =在2x =处的切线的倾斜角为5 6 π，则()2f '=. 3． ()21ln dx x x = +?. 三．计算 1．求极限 ①21lim x x x x →∞+?? ??? ②() 20sin 1 lim x x x x x e →-- 2．求曲线()ln y x y =+所确定的隐函数的导数x y '. 3．求不定积分x xe dx -?
《高等数学》练习试题库完整
华中师范大学网络教育 《高等数学》练习测试题库 一．选择题 1.函数y= 1 12+x 是（ ） A.偶函数 B.奇函数 C 单调函数 D 无界函数 2.设f(sin 2x )=cosx+1,则f(x)为（ ） A 2x 2－2 B 2－2x 2 C 1＋x 2 D 1－x 2 3．下列数列为单调递增数列的有（ ） A ．0.9 ，0.99，0.999，0.9999 B ．23，32，45，5 4 C ．{f(n)},其中f(n)=?????-+为偶数，为奇数n n n n n n 1,1 D. {n n 212+} 4.数列有界是数列收敛的（ ） A ．充分条件 B. 必要条件 C.充要条件 D 既非充分也非必要 5．下列命题正确的是（ ） A ．发散数列必无界 B ．两无界数列之和必无界 C ．两发散数列之和必发散 D ．两收敛数列之和必收敛 6．=--→1 )1sin(lim 21x x x （ ） A.1 B.0 C.2 D.1/2 7．设=+∞→x x x k )1(lim e 6 则k=( ) A.1 B.2 C.6 D.1/6 8.当x →1时，下列与无穷小（x-1）等价的无穷小是（ ） A.x 2-1 B. x 3-1 C.(x-1)2 D.sin(x-1) 9.f(x)在点x=x 0处有定义是f(x)在x=x 0处连续的（ ） A.必要条件 B.充分条件 C.充分必要条件 D.无关条件 10、当|x|<1时，y= （ ）
A、是连续的 B、无界函数 C、有最大值与最小值 D、无最小值 11、设函数f（x）=（1-x）cotx要使f（x）在点：x=0连续，则应补充定义f（0）为（） A、B、e C、-e D、-e-1 12、下列有跳跃间断点x=0的函数为（） A、 xarctan1/x B、arctan1/x C、tan1/x D、cos1/x 13、设f(x)在点x 0连续，g(x)在点x 不连续，则下列结论成立是（） A、f(x)+g(x)在点x 必不连续 B、f(x)×g(x)在点x 必不连续须有 C、复合函数f[g(x)]在点x 必不连续 D、在点x 必不连续 在区间(- ∞,+ ∞)上连续，且f(x)=0，则a,b满足14、设f(x)= （） A、a＞0,b＞0 B、a＞0,b＜0 C、a＜0,b＞0 D、a＜0,b＜0 15、若函数f(x)在点x 0连续，则下列复合函数在x 也连续的有（） A、 B、 C、tan[f(x)] D、f[f(x)] 16、函数f(x)=tanx能取最小最大值的区间是下列区间中的（） A、[0,л] B、（0,л） C、[-л/4,л/4] D、（-л/4,л/4） 17、在闭区间[a ,b]上连续是函数f(x)有界的（） A、充分条件 B、必要条件 C、充要条件 D、无关条件
高等数学下册试题及参考答案
高等数学下册试题 一、选择题（每题4分，共20分） 1. 已知A (1,0,2), B (1,2,1)是空间两点，向量 AB 的模是：（ A ） A ）5 B ） 3 C ） 6 D ）9 解 ={1-1，2-0，1-2}={0，2，-1}， |AB |= 5)1(20222=-++. 2. 设a ={1,-1,3}, b ={2,-1,2}，求c =3a -2b 是：（ B ） A ）{-1,1,5}. B ） {-1,-1,5}. C ） {1,-1,5}. D ）{-1,-1,6}. 解 (1) c =3a -2b =3{1,-1,3}-2{2,-1,2}={3-4,-3+2,9-4}={-1,-1,5}. 3. 设a ={1,-1,3}, b ={2, 1, -2}，求用标准基i , j , k 表示向量c=a-b ; （ A ） A ）-i -2j +5k B ）-i -j +3k C ）-i -j +5k D ）-2i -j +5k 解c ={-1,-2,5}=-i -2j +5k . 4. 求两平面032=--+z y x 和052=+++z y x 的夹角是：（C ） A ）2π B ）4π C ）3 π D ）π 解 由公式（6-21）有 2 1112)1(211)1(1221cos 2222222 121= ++?-++?-+?+?= ??= n n n n α， 因此，所求夹角 32 1 arccos π α= =． 5. 求平行于z 轴，且过点)1,0,1(1M 和)1,1,2(2-M 的平面方程．是：（D ） A ）2x+3y=5=0 B ）x-y+1=0 C ）x+y+1=0 D ）01=-+y x ． 解 由于平面平行于z 轴，因此可设这平面的方程为 0=++D By Ax 因为平面过1M 、2M 两点，所以有 ?? ?=+-=+020D B A D A 解得D B D A -=-=,，以此代入所设方程并约去)0(≠D D ，便得到所求的 平面方程 01=-+y x 6．微分方程()043 ='-'+''y y y x y xy 的阶数是( D )。