Following is a simple linear regression model: yi = + xi + i The following results were obtained from some statistical software.

R2 = 0.523 syx (regression standard error) = 3.028n (total observations) = 41 Significance level = 0.05 = 5%

Variable Interecpt Slope of X

Parameter Estimate 0.519

-0.707

Std. Err. of Parameter Est. 0.132

0.239

Note: For all the calculated numbers, keep three decimals.

1. Write the fitted model.

2. Make a prediction using the fitted model for y when x = 1.888

3. The intercept of the least-squares regression line is:

4. Suppose we want to test the hypotheses for the slope:

   H0: =0,H1:0

   The value of the t statistic for this test is:

5. Suppose we want to test the hypotheses for the intercept:

   H0: = 0, H1: 0

   The value of the t statistic for this test is:

6. A 95% confidence interval for the slope in the simple linear regression model is:

7.

8. 9. 10. 11.

12.

A 95% confidence interval for the intercept in the simple linear regression model is:

The correlation coefficient r between the x and y is: What is its meaning of R2?

What is the meaning of the intercept in this simple linear regression model? SST = ?

Are the intercept and slope significant at 5% significance level (Please use the hypothesis test instead of looking at the confidence intervals)?