Question 2 (7 marks)

Assume you have noted the following prices for books and the number of pages that each book contains.

Book	Price (in $) Y	Pages X
A	7.00	500
B	7.50	700
C	9.00	750
D	6.50	590
E	7.50	540
F	7.00	650
G	4.50	480

A part of the output of a regression analysis of Y against X using Excel is given below:

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.75027
R Square	0.56290
Adjusted R Square	0.475487
Standard Error	0.980614
Observations	7
ANOVA
	df	SS	MS	F	Significance F
Regression	1	6.191972	6.191972
Residual	5	4.808028	0.961606
Total	6	11
	Coefficients	Standard Error	t Stat	P-value
Intercept	1.04155	2.37717
Pages	0.00990	0.00390

1. State the estimated regression line and interpret the slope coefficient. (1 mark)
2. What is the estimated total price when a book has ONE THOUSAND pages? (1 mark)
3. What is the value of the coefficient of determination? Interpret it. (1 mark)
4. Test whether there is a significant relationship between price and pages at the 10% significance level. Perform the test using the following six steps. (4 marks)

Step 1. Statement of the hypothesis (0.5 mark)

Step 2. Standardised test statistic (0.5 mark)

Step 3. Level of significance (0.5 mark)

Step 4. Decision Rule (1 mark)

Step 5. Calculation of test statistic (1 mark)

Step 6. Conclusion (0.5 mark)

ANSWER:

Question 2 (7 marks) Assume you have noted the following prices for books and the number of pages that each book contains. \"\"5\" part of the output of a regression analysis of Y against X using Excel is given below: SUMMARY OUTPUT Regression Statistics Multiple R 0.75027 R Square 0.56290 Adjusted R Square 0.475487 Standard Error 0.980614 Observations 7 ANOVA df 55 MS F Significance F Regression 1 6.191972 6.191972 H|6007 Final Assessment T1 2022 Residual 4.808028 0.961606 Total 11 Coefficients Standard Error t Stat P-value Intercept 1.04155 2.37717 Pages 0.00990 0.00390 A. State the estimated regression line and interpret the slope coefficient. (1 mark) B. What is the estimated total price when a book has 1000 pages? (1 mark C. What is the value of the coefficient of determination? Interpret it. (1 mark) D. Test whether there is a significant relationship between price and pages at the 10% significance level. Perform the test using the following six steps. (4 marks) Step 1. Statement of the hypothesis (0.5 mark) Step 2. Standardised test statistic (0.5 mark) Step 3. Level of significance (0.5 mark) Step 4. Decision Rule (1 mark) Step 5. Calculation of test statistic (1 mark) Step 6. Conclusion (0.5 mark)