Question

In Regression Analysis, you are given the following information:

Y = 21.33 + 9.67x

SSE = 573 SSR = 4498

1. Predict the value of y if X = 4    . (2 decimal places)

2. Calculate the coefficient of determination  . (2 decimal places)

3. Is the following statement true or false?

The coefficient of determination is the proportion of the variation in y that is not explained by the variation in x.   

4. Based upon the Coefficient of Determination, if this regression equation represented data for a safety issue, what would you recommend be done to improve the equation results?

5. y = 21.33 + 9.67x - 10.02w

Predict the value of y if x = 3 and w = -2      (2 decimal places)

Please do not ignore part 3 and 4.

Thanks

Answer 1

1) predicted y-hat =   =21.33+9.67*4 =   60.01

2) R^2 = SSR/SST = SSR/(SSE+SSR)   =4498/(573+4498) =   0.89

3) the coefficient of determination tells the % of variation in the dependent variable which is expalined by all independent variables in model.      
hence, given statement that "The coefficient of determination is the proportion of the variation in y that is not explained by the variation in x. " is FALSE.      

4) There is 89% variation in Y which is explained by X. hence fiited model is a good fit for the data.      
but in order to improve the results, transformations can be used. Addition of other signficicant independent variables could also improve the equation results.

   
5) predicted yhat =   =21.33+9.67*3-10.2*-2 =   70.74