Question

Please open “LIFE” data. The data is related to results of a survey that asks people to grade themselves in terms of Conscientiousness and Life satisfaction. Conscientiousness grading scale is from 1 to 10 whereas Life satisfaction criteria was graded from 1 to 80. And each person, surveyed grade himself by own for both criteria. Gender information is included in data as well. The objective of survey is whether life satisfaction can be explained with conscientiousness and gender. So, the dependent variable is defined as life satisfaction and the independent variables are gender and conscientiousness. Please do the following steps:

1) Test if conscientiousness has no significant effect on life satisfaction at alpha=0.05 significance level.

2) Give a complete interpretation of the slope coefficient of conscientiousness.

3) Find Adjusted R^2 and give a complete interpretation.

4) Create a plot that shows how residuals vary by predicted values (ZRESID vs ZPREDIC)

  LIFE DATA

Conscientiousness	Life Satisfaction	Gender(1 Female, 0 Male)
6	45	0
5	30	1
2	38	1
1	50	0
2	30	1
5	34	1
2	40	0
7	57	0
2	35	0
7	51	0
5	30	0
6	39	1
2	40	1
5	30	0
3	10	0
2	40	1
1	45	0
3	14	0
7	54	1
1	50	1
5	31	0
6	43	1
5	27	1
7	51	0
7	50	1
7	51	0
4	10	0
5	34	0
5	28	1
2	35	0

Answer 1

1) Test if conscientiousness has no significant effect on life satisfaction at alpha=0.05 significance level.

Ans: The p-value for the significance test of slope corresponding for the independent variable conscientiousness is 0.156. This p-value is greater than the alpha=0.05 significance level. Hence, we can conclude that conscientiousness has no significant effect on life satisfaction at the alpha=0.05 significance level.

2) Give a complete interpretation of the slope coefficient of conscientiousness.

The estimated slope for the variable conscientiousness is  1.571. Hence, when a unit increase for the variable conscientiousness, it increases the mean of life satisfaction by 1.571.

3) Find Adjusted R^2 and give a complete interpretation.

Ans: The Adjusted R^2 value is 1.3%. Hence, only 1.3% variation of the model is explained by the significant explanatory variables.

4) Create a plot that shows how residuals vary by predicted values (ZRESID vs ZPREDIC)

Ans:

From the above residuals VS predicted (FITS1) values plot, the value of the residuals increases when the value of the predicted decreases from the left side up to the middle of the plot. After some points, the value of the residuals increases when the corresponding value of the predicted increases from the middle to the right side. Hence3, we can say that residuals are vary by predicted values.