Following is a simple linear regression model:

^yi = _{0 + 1}x_{i + i}

The following results were obtained from some statistical software. R2 = 0.675

syx (regression standard error) = 4.199

n (total observations) = 55

Significance level = 0.05 = 5%

Variable	Parameter Estimate		Std. Err. of Parameter Est.
Intercept		0.830		0.275
Slope of X		-0.818		0.313

Note: 1. For all the calculated numbers, keep three decimals.

2. For calculation-related questions, show the formulas and the major calculation procedures for full credit.

1. Write the fitted model (5 points).

2. Make a prediction using the fitted model for y when x = 2.107 (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: ₁ = 0, H1: ₁ 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 = 0, H1: ₀ 0 The value of the t statistic for this test is (10 points):

6. A 95% confidence interval for the slope ₁ in the simple linear regression model is (10 points):

7. A 95% confidence interval for the intercept ₀ 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)?