Question

# Examine the Minitab output shown here for a multiple regression analysis. How many predictors were there...

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

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.