Question

Examine the Minitab output shown here for a multiple regression analysis. How many predictors were there in this model? Comment on the overall significance of the regression model. Discuss the t ratios of the variables and their significance.

The regression equation is

y = 4.091 - 5.111x₁+ 2.662x₂ + 1.557x₃ + 1.141x₄ +1.655x₅ - 1.248x₆ + 0.436x₇ + 0.959x₈ + 1.289x₉

Predictor	Coef	Stdev	T	p
Constant	4.096	1.2884	3.24	.006
x1	-5.111	1.8700	2.73	.011
x2	2.662	2.0796	1.28	.212
x3	1.557	1.2811	1.22	.235
x4	1.141	1.4712	0.78	.445
x5	1.655	1.4994	1.10	.281
x6	-1.248	1.2735	0.98	.336
x7	0.436	0.3617	1.21	.239
x8	0.959	1.1896	0.81	.426
x9	1.289	1.9182	0.67	.508

S = 3.437    R-sq = 40.8%    R-sq(adj.) = 21.1%

Analysis of Variance

Source	DF	SS	MS	F	p
Regression	9	219.746	24.416	2.07	0.0697
Error	27	319.004	11.815
Total	36	538.750

Answer 1

If we look at the Minitab output for this model, we can see that there are 9 predictors, i.e. x1, x2, x3, x4, x5, x6, x7, x8 and x9

The overall F statistic value and its corresponding p value at 0.05 significant level is not significant because the p value is greater than 0.05 significance level. So, we can not use this model for the prediction of dependent variable using all the nine independent variables because the F statistic and p value are not significant at 0.05 signifcance level.

If we look at the individual t values and p values corresponding to all the nine predictors, it is clear that not a single predictor is signifcant at 0.05 significance level because the p values for all 9 predictors are greater than 0.05 level.

So, there is no significant predictor.