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Assume you have noted the following prices for books and the number of pages that each book contains. Book Price (in $) Y Pages X
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 | |||||||||
- State the estimated regression line and interpret the slope coefficient.
- What is the estimated total price when a book has 1000 pages?
- What is the value of the coefficient of determination? Interpret it.
- Test whether there is a significant relationship between price and pages at the 10% significance level. Perform the test using the following six steps.
Step 1. Statement of the hypothesis
Step 2. Standardised test statistic
Step 3. Level of significance
Step 4. Decision Rule
Step 5. Calculation of test statistic
Step 6. Conclusion
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