Question

4. Data on the unemployment rate and alcohol sales were analyzed. The following regression equation was computed from a sample of 18 data points.

?̂ = 3 . 5 9 + . 7 2 ?

(A) Complete this ANOVA table. (9)

Source	SS	df	MS	F
Regression
Error	301.1
Total	403.8

(B) Determine the standard error of estimate. (Round to 3 decimals.) (9)

(C) Determine the coefficient of determination. (Round to 3 decimals.) (9)

(D) Determine the correction coefficient. Clearly indicate the sign. (Round to 3 decimals.) (5)

(E) Draw a picture of what this regression would look like on a scatterplot. (8)

Explain, based on the coefficient of determination, whether we can reliably say something about alcohol sales based on information from unemployment statistics. Be sure to clearly articulate what the coefficient of determination is conceptually, in your own words and using the terms of this example!

Answer 1

Solution-A

df regression=k=1

df error=n-k-1=18-1-1=16

MS regression=SS regression/df regression

MS error=SS error/df error

F=MS regression/MS error

Solution-B:

Standard error of estiamte=sqrt(MSE)=sqrt(18.81875)= 4.338058=4.338

Se=4.338

Solution-c:

R sq=SS Regression/SS total

=102.7/403.8

= 0.2543338

=0.254

R sq=0.254

Solution-d:

correlation coeffcient=sqrt(R sq)

=sqrt(0.2543338)

= 0.5043152

0.504

r=0.504

since slope is positive

r=+0.504

correlation coeffcient,r=+0.504