## Related questions with answers

Based on a sample of 25 observations, the population regression model

$y_i=\beta_0+\beta_1 x_1+\varepsilon_i$

was estimated. The least squares estimates obtained were as follows:

$b_0=15.6 \text { and } b_1=1.3$

The total and error sums of squares were as follows:

$S S T=268 \text { and } \quad S S E=204$

a. Find and interpret the coefficient of determination.

b. Test, against a two-sided alternative at the $5 \%$ significance level, the null hypothesis that the slope of the population regression line is 0 .

c. Find a $95 \%$ confidence interval for $\beta_1$.

Solution

Verified**(a)** Calculate the coefficient of determination $R^2$ by using the formula below.

$R^2=1-\frac{SSE}{SST}$

where $SSE$ is the sum of squares error and $SST$ is the sum of squares total.

Plug in the values $SSE=204,SST=268$ to the formula above.

$R^2=1-\frac{204}{268}$

Simplify by applying PEMDAS rules.

$\begin{aligned} R^2&=1-0.76\\ &=\boxed{0.24} \end{aligned}$

The coefficient of determination $R^2$ is equal to $0.24$. The higher the value of the coefficient of determination, the better the regression.

## Create an account to view solutions

## Create an account to view solutions

## Recommended textbook solutions

#### Applied Statistics in Business and Economics

3rd Edition•ISBN: 9780073373690 (2 more)David Doane, Lori Seward#### Applied Statistics in Business and Economics

5th Edition•ISBN: 9780077837303David Doane, Lori Seward#### Statistics for Business and Economics

8th Edition•ISBN: 9780132745659 (11 more)Betty Thorne, Paul Newbold, William Carlson#### Statistics for Business and Economics

13th Edition•ISBN: 9781305585317 (8 more)David R. Anderson, Dennis J. Sweeney, James J Cochran, Jeffrey D. Camm, Thomas A. Williams## More related questions

1/4

1/7