3. Based on the multiple regression using the number of sessions attended and be

Question

3. Based on the multiple regression using the number of sessions attended and beginning weight, which of the following apply? (Check any as appropriate.)

a. When included with beginning weight, number of sessions attended becomes insignificant in the model.

*b. At the 5% level of significance, beginning weight is a useful explanatory variable.

c. Clients with higher beginning weights tended to lose more weight.

d. The overall model explains more than 50% of the variation in weight loss.

e. Based on adjusted R2, we would prefer the model using only the number of sessions.  

f. There is severe multicollinearity present.

Here is the data:

Client Loss Sessions Weight 1 7 5 185 2 17 7 215 3 -2 3 148 4 8 5 166 5 29 6 197 6 -6 4 153 7 4 5 182 8 15 8 184 9 11 3 155 10 22 6 207 11 -7 2 238 12 12 5 214 13 8 4 195 14 -3 5 179 15 6 3 194 16 13 7 187 17 11 5 227 18 6 5 202 19 7 3 198 20 -4 4 217 21 0 4 183 22 5 5 196 23 8 7 210 24 18 8 247 25 12 5 223 26 4 5 216 27 33 6 242 28 -9 3 169 29 7 5 205 30 14 6 207 31 6 4 176 32 10 5 194 33 5 6 189 34 12 3 213 35 -4 2 228 36 7 5 199 37 9 4 196 38 6 3 187 39 3 5 172 40 1 3 165

Explanation / Answer

Based on the multiple regression model given above, only the following condition holds true: -

c. Clients with higher beginning weights tended to lose more weight.

SUMMARY OUTPUT Regression Statistics Multiple R 0.656 R Square 0.431 Adjusted R Square 0.400 Standard Error 6.843 Observations 40 ANOVA df SS MS F Significance F Regression 2 1309.63 654.81 13.99 0.00 Residual 37 1732.35 46.82 Total 39 3041.98 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept -25.55 9.19 -2.78 0.01 -44.18 -6.92 Sessions 3.25 0.75 4.31 0.00 1.72 4.77 Weight 0.09 0.05 1.90 0.07 -0.01 0.19

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