Interpreting Simple Linear Regression

1. Linear correlation coefficient r = 0.794556

2. Coefficient of Determination ( r square) 0.631319

3. Standard Error of the estimate = 12.9668

4. SSR (Explained variation) = 5182.41

5. SSE ( Unexplained variation) = 3026.49

6. SST = 8208.90

7. Predicted equation or equation of the regression line (Y predicted or hat) = 0.725983X + 16.5523

8. Level of Significance = 0.1

9. Critical Value= 0.378419

10. t test = 0.794556

Question

a. What is meant by a hypothesis? What is the null hypothesis in this example

b. What is the meant by the standard error of the estimate? Which number measures the scatter of points about the regression line?

c. Define the Y intercept of the regression line. What is the Y intercept?

d. How the test whether the Null Hypothesis should be rejected or not?

e. Which number measures the distances from the prediction line to the actual values?

f. Question : Are the variables moving in the same direction. If yes why? If no, why?

g. Which number is the allowable risk of making a Type I error?

h. What is meant by the slope of the regression line? Which number is the slope of the regression line?

i. What is meant by SSR? Which number measures the variation explained by the regression line?