DSC 5100 Quantitative Methods

Homework Assignment #2 - Module 2

UNC Pembroke

Instructor: Dr. Zhixin (Richard) Kang

Following is a simple linear regression model:

The following results were obtained from some statistical software.

R² = 0.523

s_yx (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: b ₁ = 0, H₁: b₁ 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: b ₀ = 0, H₁: b ₀ 0

The value of the t statistic for this test is (10 points):

6.

A 95% confidence interval for the slope b₁ in the simple linear regression model is (10 points):

7.

A 95% confidence interval for the intercept b 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)?