Using question 12 (delaying major purchases) as the response variable (Y) comput

Question

Using question 12 (delaying major purchases) as the response variable (Y) compute a regression model with the following questions 9, 25 (gender: males as 0 and females coded as 1) as your predictor variables.

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Find:

Excel Output

Model: write down model like in form y = b0 + b1X1 +b2X2 +…+ bkXk using Excel output to put in actual coefficients.

Interpret the slope coefficient: Report and interpret the slope coefficient for variable q25 (gender).

Predictiveness of variable q25 (gender): Determine whether q25 is predictive of Y using both the p-value and confidence interval approaches. Use alpha = .05 for p-value and 95% for confidence interval.

R2: Report and interpret the explanatory power of model.

Prediction: What does the model predict for Y when gender =1, q9=7.

Gender 1 0 0 0 1 1 1 1 1 0 1 0 0 0 1 1 1 1 1 0 1 0 0 0 1 1 1 1 1 0 1 0 0 0 1 1 1 1 1 0 1 0 0 0 1 1 1 1 1 0 1 0 0 0 1 1 1 1 1 0 1 0 0 0 1 1 1 1 1 0 1 0 0 0 1 1 1 1 1 0 1 0 0 0 1 1 1 1 1 0 1 0 0 0 1 1 1 1 1

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Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 90.0% Upper 90.0% Intercept -38.2073 2.422993 -15.7686 2.86E-28 -43.01751187 -33.397 -42.232 -34.1825 Gender -11.3011 1.367858 -8.26193 8.42E-13 -14.01669012 -8.58561 -13.5732 -9.02906

Explanation / Answer

Solution- Regression equation is -

y = -38.2073 -11.3011 X

Where y = response variable and x = gender

Hypotheses would be -

H0: Slope equal to zero

Ha: Slope not equal to zero

P-value from the table is equal to 8.42E-13.

This is less than 0.05 hence null hypothesis is rejected and thus model is significant.

R2 means that percantage of total variation in the response variable explained by the independent variable in the model.

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