Question

1. Based on the regression output obtained in Step 4, answer the following:

1. Which summary measure in the regression output is used to assess the overall adequacy of the model? Comment on the overall adequacy of the model obtained in Step 4 for each of the three dependent variables.

Independent Variable	Model Significance	R-Squared	Adjusted R-Squared	β0 (Intercept)	β1 (Gender)	β2 (Age)	β3 (Lives at Home)	β4 (Year 10)	β5 (Year 12)	β6 (Bachelor)
Instagram – Step 4	6.443-13	0.102	0.093	80.321	5.612	-0.905	-2.977	-11.500	-7.491	-5.831
Facebook – Step 4	0.535	0.008	-0.001	51.630	-1.343	-0.547	0.234	-0.561	-1.498	0.795
Other – Step 4	0.917	0.003	-0.006	54.531	-0.134	-0.278	0.733	-0.584	0.299	0.024

If < 0.05 – Green, If between 0.05 < 0.1 – Blue, if > 0.1 – Purple, Overall Adequacy - Yellow.

b. For each of the independent variables, fully interpret the regression coefficients and comment on their statistical significance. (In discussing statistical significance of a regression coefficient, you have to justify your choice of one or two tail test.)

Answer 1

a.

The overall adequacy of the model can be assessed using the Goodness of Fit measure 'Coefficient of Determination' R2, which the the amount of explained variation in the model. For more than one predictor in the model. However, a better measure would be adjusted R2 , which not only indicates how well terms fit a curve or line, but also adjusts for the number of terms in a model. Every time a non significant predictor is added to the model, R2 simply increases, but, adjusted R2 will decrease. If we add significant variables, adjusted r-squared will increase.

Comparing the adjusted R2 for the three dependent variables, (Adj R2 = 9.3% for Instagram, Adj R2 = -0.1% for Facebook, Adj R2 = -0.6% for Other)

We find that the predictors of the model for predicting the response 'Instagram' explains the maximum variation.

b.

Assuming that the significance level for the test is fixed at 5% (say):

For Model 1:

We find that the intercept and the slopes of all the predictors in the model except Age (β2 = -0.905) are significant in predicting the response (dependent) variable.

The mean value of the response variable Instagram when values of all the predictors in the model are zero is 80.321.

- The expected mean difference in 'Instagram' variable between Men and Women is 5.612 - The expected mean difference in 'Instagram' variable for a person who does and does not live at home is -2.977 - For every unit increase in 'Year10', 'Year12' and 6th predictor, the response variable decreases by -11.5, -7.491 and the slope coefficient for the predictor (the figure in the question has not been displayed completely) respectively.

For Model 2:

We find that the Intercept alone is significant (β0 = 51.630) is significant in predicting the response (dependent) variable.

The mean value of the response variable 'Facebook' when values of all the predictors in the model are zero is 51.630. This suggests that this model with no significant predictors is a poor fit to the data.

For Model 3:

We find that the Intercept alone is significant (β0 = 54.531) is significant in predicting the response (dependent) variable.

The mean value of the response variable 'Other' when values of all the predictors in the model are zero is 54.531. This suggests that this model with no significant predictors is a poor fit to the data.