If all the points of a scatter diagram lie on the least squares regression line,

Question

If all the points of a scatter diagram lie on the least squares regression line, then the coefficient of determination for these variables based on this data is

Select one:

A. 0

B. 1

C. either 1 or -1, depending upon whether the relationship is positive or negative

D. could be any value between -1 and 1

E. None of the above is correct answer

Question 13

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Regression analysis was applied between sales data (in $1,000s) and advertising data (in $100s) and the following information was obtained: y=12+1.8x, n=17, SSR=225, SSE=75, and Sb=0.2683. Based on the information provided, if advertising is $3,000, then the point estimate for sales (in dollars) is

Select one:

A. $66,000

B. $5,412

C. $66

D. $17,400

E. None of the above answers is correct

Question 14

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Reference sales problem statement above, what is the calculated t statistic for testing the significance of the slope?

Select one:

A. 1.80

B. 1.96

C. 6.709

D. 0.555

E. None of the above answers is correct

Question 15

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Select one:

E. 1.753

F. -2.131

G. 2.131

H. None of the above answers is correct

Question 16

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Reference sales problem statement above, if the t statistic based on sample data is greater than the critical value(s) for t based on significance level then, which of the following is a correct statement?

Select one:

A. the relationship between x and y is statistically significant

B. the relationship between x and y is not statistically significant

C. linear regression equation is not adequate to statistically describe the mathematical relationship between x and y, therefore, a higher order equation should be used

D. None of the above statements is correct

Question 17

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Commercial Carpet Inc. is specialized in selling carpet to commercial businesses. The manager of the store conducts a five month experiment to determine the effect of advertising on sales revenue. The results are tabulated below:

Use the least square method to come up with the best linear line fitting this data. What are the slope and y-intercept for the linear equation based on least sqaure method?

Select one:

A. slope=0.95, y-intercept=-0.2

B. slope=0.7, y-intercept=-0.1

C. slope=-0.1, y-intercept=0.7

D. slope=1.2, y-intercept=0.3

E. None of the above answers is correct

Question 18

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Reference Commercial Carpet problem statement, for $300 in advertising expenditure, how much is the corresponidng sales revenue?

Select one:

A. $2650

B. $2000

C. $400

D. $3900

E. $209.90

F. None of the above answers is correct

Question 19

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Reference Commercial Carpet problem statement, what percentage of data is explained by regression equation?

Select one:

A. 100%

B. 0%

C. 88.6%

D. 34.5%

E. 81.67%

Question 20

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Reference Commercial Carpet problem statement, using t-test and significance level of 5%, is the linear relationship described by regression equation based on the least square method statistically significant?

Select one:

A. reject null hypothesis, the linear relationship described by regression equation is statistically significant

B. don't reject null hypothesis, the linear relationship described by regression equation is not statistically significant

C. reject null hypothesis, the linear relationship described by regression equation is not statistically significant

D. don't reject null hypothesis, the linear relationship described by regression equation is statistically significant

E. None of the above answers is correct

Month Advertising Expenditure ($100s) Sales Revenue ($1000s) 1 1 1 2 2 1 3 3 2 4 4 2 5 5 4

Explanation / Answer

If all the points of a scatter diagram lie on the least squares regression line, then the coefficient of determination for these variables based on this data is 1. Because here the correlation coefficient will be 1, so the coefficient of determination or r^2 will be 1.

Based on the information provided, if advertising is $3,000, then the point estimate for sales (in dollars) is y(3000)=12+1.8*3000=$5412

The t test statistic is: sb/b1=0.2683/1.8=6.709

The critical t values are: t(n-2,0.05)=t(17-2,0.05)=t(15,0.05)=+/-2.131

Since the test statistic falls in the critical region, reject the null hypothesis. So, A. the relationship between x and y is statistically significant.

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