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) = 3.028 n (total observations) = 41 Significance level = 0.05 = 5% Variable Parameter Estimate Std. Err. of Parameter Est. Interecpt 0.519 0.132 Slope of X -0.707 0.239 Note: For all the calculated numbers, keep three decimals. 1. Write the fitted model (5 points). 2. Make a prediction using the fitted model for y when x = 1.888 (5 points) 3. The intercept of the least-squares regression line is (5 points): 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 (10 points): 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 (10 points): 6. A 95% confidence interval for the slope  in the simple linear regression model is (10 points): 7. A 95% confidence interval for the intercept  in the simple linear regression model is (10 points): 8. The correlation coefficient r between the x and y is (10 points): 9. What is its meaning of R2 (10 points)? 10. What is the meaning of the intercept in this simple linear regression model (5 points)? 11. SST = ? (10 points) 12. Are the intercept and slope significant at 5% significance level (Please use the hypothesis test instead of looking at the confidence intervals) (10 points)?