Question

Results for: KCereals.mtw

Regression Analysis: Rating versus Shelf position

Method

Categorical predictor coding (1, 0)

Analysis of Variance

Source DF Adj SS Adj MS F-Value P-Value
Regression 2 1511 755.6 5.50 0.013
Shelf position 2 1511 755.6 5.50 0.013
Error 20 2748 137.4
Total 22 4259

Model Summary

S R-sq R-sq(adj) R-sq(pred)
11.7222 35.48% 29.03% 21.34%

Coefficients

Term Coef SE Coef T-Value P-Value VIF
Constant 32.85 4.43 7.41 0.000
Shelf position
bottom 7.40 7.35 1.01 0.326 1.30
top 18.15 5.58 3.26 0.004 1.30

Regression Equation

Rating = 32.85 + 7.40 Shelf position_bottom + 0.0 Shelf position_middle
+ 18.15 Shelf position_top

Fits and Diagnostics for Unusual Observations

Std
Obs Rating Fit Resid Resid
13 93.70 51.00 42.71 3.81 R

R Large residual

————— 4/25/2019 8:34:40 PM ————————————————————

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Results for: KCereals.mtw

Regression Analysis: Rating versus Shelf position

Method

Categorical predictor coding (1, 0)

Analysis of Variance

Source DF Adj SS Adj MS F-Value P-Value
Regression 2 1511 755.6 5.50 0.013
Shelf position 2 1511 755.6 5.50 0.013
Error 20 2748 137.4
Total 22 4259

Model Summary

S R-sq R-sq(adj) R-sq(pred)
11.7222 35.48% 29.03% 21.34%

How do I do the model utility test for this data?

Does it involve the null and alternative hypothesis or the F-test? If so, how do I perform it?

Answer 1

Here we want to test in regression that regression model is worth or not.

In F-test we are trying to do the testing that as a whole the regression is working or not.

So in F-test the hypothesis is

H0 : all coefficient of regression is zero

Vs

H1 : at least one coefficient is not zero.

And this test results will come from ANOVA table as

We can note the p-value corresponding regression of ANOVA table is 0.013<0.05 hence reject H0 we can comment that the regression is working significantly.