Question

1) Please find the partially completed multiple regression analysis below, which explores the relationship betwen the sales (in hundreds) and the independent variables price(in dollars), promotional expenditure(in hundreds of dollars) and the quality score (0-100) for a very popular Cbristmas season toy The regression equation is Sales -3432-0.23 Price + 2.7" Promotional exp + 0.22 Quality Predictor Constant Price Promotional exp 2.704 Quality Coef Standard Errorl SE Coef T P VIF 343.20 62.59 -0.23358 0.0373 2.415 1.047 10.387 0.2204 0.1429 R-Sq = Analysis ot Variance Source Regression Residual Error Total DF SS MS F 2847.78 15 3933.40
Based on the anova presented perform the overall f test and state if the regression is significant a=.05

Answer 1

As there are three predictors: price, promotional expense and quality, the DF of Regression will be 3.

So, Residual Error DF = Total DF - Regression DF = 15 - 3 = 12

SS of Residual Error = SS Total - SS Regression = 3933.40 - 2847.78 = 1085.62

MS Regression = SS Regression / Regression DF = 2847.78 / 3 = 949.26

MS Residual Error = SS of Residual Error / Residual error DF = 1085.62 / 12 = 90.468

Completing ANOVA Table

Source	DF	SS	MS	F
Regression	3	2847.78	949.26	949.26 / 90.468 = 10.493
Residual Error	12	1085.62	90.468
Total	15	3933.40

Tabulated F value,

$F_{\alpha, df1, df2} = F_{0.05, 3, 12} = 3.49$

So, as the calculated F value (10.493) is greater than tabulated F value (3.49) we reject the null hypothesis and conclude that the regression is significant.