Reference no: EM13243484

1. Use the following results obtained from a simple linear regression analysis with 12 observations.

 Y^  = 37.2895 - (1.2024)X

r² = 0.6744  and s_b1 = 0.2934
Test to determine if there is a significant negative relationship between the independent and dependent variable at a =.05 and .01

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 6 months of data consisting of tire sales (in thousands of tires) and advertising expenditures (in thousands of dollars). Based on the data set with 6 observations, the simple linear regression model yielded the following results. (X is advertising expenditure in thousand dollars and Y is tires sold in thousands): ∑X =24; ∑Y =42; ∑X² = 124; ∑Y² = 338; ∑XY = 196

Find the Intercept and slope and Write the Regression Equation. Also predict the amount of tires (in thousand tires) sold when money invested in advertising is 5 thousand dollars. Calculate the correlation coefficient, coefficient of determination. Check whether there is a relation between correlation coefficient and coefficient of determination. Calculate SSE and MSE and standard error of the slope coefficient.

3. Consumer Reports provided extensive testing and ratings for more than 100 HDTVs. An overall score, based primarily on picture quality, was developed for each model. In general, a higher overall score indicates better performance. The following data show the price and overall score for the ten 42-inch plasma televisions (Consumer Report data slightly changed here):

Use the above data to develop an estimated regression equation. Compute the Coefficient of Determination and the correlation coefficient and show their relation. Interpret the explanatory power of the model. Estimate the overall score for a 42-inch plasma television with a price of $3400.