1. Use the following results obtained from a simple linear regression analysis with 15 observations.
Y ^ = 35.5- (1.75)X
R2= 0.9345 and sb1 = 0.60
Interpret regression results and the value of the coefficient of Determination. Predict the value of Y when X is equal to 10. Calculated the correlation coefficient between Y and X. Test to determine if there is a significant relationship between the independent and dependent variable at ? = 0.05. Perform a two-tailed test.
2. A local tire dealer wants to predict the number of tires sold each month. He believes that the number of tires sold is a linear function of the amount of money invested in advertising. He randomly selects past months of data consisting of tire sales (in hundreds of tires) and advertising expenditures (in thousands of dollars). Based on the data set with 20 observations, the simple linear regression model yielded the following results. (X is advertising expenditure in thousand dollars and Y is tires sold in hundreds): ∑X = 50; ∑Y = 100; ∑X2 = 225; ∑Y2 = 720; ∑XY = 390.
Find the Intercept and slope and Write the Regression Equation. Also predict the amount of tires sold when money invested in advertising is 5 thousand dollars. Calculate the correlation coefficient and coefficient of determination. Check whether there is a relation between correlation coefficient and coefficient of determination. Calculate SSE and MSE, and standard error and t-score of the slope coefficient.