Question

1. You are interested in examining the relationship between BMI (continuous on (continuous variable), and gender (variable"woman" coded as O man and 1 - variable), years of woman) among a sample of 300 25-35 year olds. You first want to estimate a regression model that includes the independent associations of years of education and gender with BMI. Next, you will estimate a model in which gender moderates the association between BMI and years of education a. First, write the equation of the multiple regression model with only main effects. Then, write the equation of the multiple regression model with the interaction term. (1pt) b. Using the following regression table: BMI I Coef. Std. Err. t P>It] [95% Conf. Interval! 0338 -3.11 0.002 180 0.02 0.984 466 63.43 0.000 .171-038 -350 357 28.656 30.484 Years Edu 1 -105 Woman 1 .004 Intercept 29.57 Write out the main effects regression model equation using values for the coefficients.(0.5pt) i. Identify which predictor variable(s) is statistically significantly associated with BMI. Explain why. (0.5pt) ii. ili. Estimate the BMI of a woman who has 12 years of education. (0.5pt) Using the following regression table with the years of education: c. n term between gender and P>ltl 0.050.960 3.100.002 -3.16 0.002 0.000 BMI Coef. Std. Err. t 195% -094 089 1.026 4.552 I -002 I 2.789 046 -899 067 632 44.58 Years Edu Woman Woman Years Edu 1 -213 -346-081 26.974 29.455 Intercept 28.215 i Write out the regression model equation using values for the coefficients. (0.5pt) Does gender moderate the relationship between BMI and years of education? Explain why or why. If you conclude that gender is a moderator, interpret the coefficient for the interaction term. (1pt) li.

Answer 1

Answer a)

Main effect Regression Equation

BMI = B0 + B1*Years_Edu + B2*Woman

Regression Equation with Interaction Term

BMI = B0 + B1*Years_Edu + B2*Woman + B3*Years_Edu*Woman

Answer b)

i)

Substituting values of regression coefficients from table, we get following main effect regression equation:

BMI = 29.57 - 0.105*Years_Edu + 0.004*Woman

ii)

Years of Education is the statistically significant predictor of BMI. This is because p-value corresponding to its regression coefficients is 0.002 which is less than 0.05.

ii)

BMI of Woman with 12 years of education can be obtained by substituting Woman = 1 and Years_Edu = 12 in regression equation:

BMI = 29.57 - 0.105*12 + 0.004*1

BMI = 28.314

Answer c)

i)

Substituting values of regression coefficients from table, we get following regression equation with interaction Term:

BMI = 28.215 - 0.002*Years_Edu + 2.789*Woman - 0.213*Years_Edu*Woman

ii)

From man (Women = 0) regression equation is as follows:

BMI = 28.215 - 0.002*Years_Edu

From woman (Women = 1) regression equation is as follows:

BMI = 28.215 - 0.002*Years_Edu + 2.789*1 - 0.213*Years_Edu*1

BMI = 31.004 - 0.215*Years_Edu

From the regression equation, we can seen that 1 unit increase in years of reduction decreases BMI of man by 0.002 units while women by 0.215 units. Thus, it can be said that gender moderates the relationship between BMI and years of education.

The p-value of coefficient of interaction term is 0.002, which is less that 0.05. So it can be said the interaction term is statistically significant.