Based on the regression output obtained in Step 4, answer the following question

Question

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

1. Comment on the overall adequacy of the model.

2. For each of the four independent variables, interpret the regression coefficients and comment on their statistical significance.

STEP 4 of Regression below:

SUMMARY OUTPUT Regression Statistics Multiple R 0.3443249 R Square 0.11855963 Adjusted R Square 0.11215382 Standard Error 11.6065301 Observations 694 ANOVA df SS MS F Significance F Regression 5 12466.2881 2493.25762 18.5081219 2.8497E-17 Residual 688 92681.5403 134.711541 Total 693 105147.828 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 24.3353258 2.4438524 9.95777235 6.5142E-22 19.537022 29.1336297 19.537022 29.1336297 Gender (M=1) -1.35726657 0.88931329 -1.52619621 0.12742057 -3.10336032 0.38882717 -3.10336032 0.38882717 Degree type (Single=1) -5.71516895 0.9914719 -5.76432773 1.2378E-08 -7.66184275 -3.76849516 -7.66184275 -3.76849516 Country (Australia=1) 2.77254421 2.05591923 1.3485667 0.17791992 -1.26408466 6.80917308 -1.26408466 6.80917308 Country (East Asia=1) 9.90598056 2.23926222 4.42376979 1.1273E-05 5.50937275 14.3025884 5.50937275 14.3025884 Lecture Attendance 0.71466509 0.15700913 4.55174218 6.2904E-06 0.40639053 1.02293965 0.40639053 1.02293965

Explanation / Answer

Answer to the question is as follows:

1.

The model is sigificant with a p-value of 2.8497E-17 which is less than .05

But the overall Rsquare is .118 which is quiet small, indicating the model is not adequate in terms of
variable captured to predict the dependent variable. Only 11.2% of the variance in depednent variable can be explained

2. Each of the independent variables except Gender (Male=1) is statistically significant as they all have
p-value smaller than .05

For a unit increase in Lecture attendance dependent variable increases by .715
If the country is an East Asia country, the dependent variable increases by 9.906
If the country is australia , the dependent variable increases by 2.773
If the degreee is single, then the dependent variable decreases by -5.715
If the gender is male then the dependent variable decreases by 1.357 units

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