Question

1. Dummy Variable Regression: Choose any metric variable as the dependent variable (you can use the same one that you used in Part A) and choose gender as an independent variable. Also choose one more metric variable as an additional independent variable. Once again, however, you must sort through the metric independent variables until you find one that, along with gender, produces a significant F-calc. Use alpha = .05 here as well.   You only need to report the model that produced a significant F-calc and not those you had to sort through to find it. Again, interpret the model as in Part A by providing the equation and an interpretation of the other diagnostic values.

Please interpret the rest of the model (r², adjusted r², t-calcs, confidence intervals) and type out the model in the form of y = b₀ + b₁x₁ + b₂x₂ + b₃x₃ putting in the actual estimates and names of the variables used.

Regression Variables Entered/Removeda Variables Variables Model Entered Removed Method Gender Enter a. Dependent Variable: Listens b. All requested variables entered Model Summary Adjusted R Square Std. Error of the Model R Square Estimate 213a 046 042 1.965 a. Predictors: (Constant), Gender ANOVA Model Sum of Squares 50.511 1058.398 1108.909 df Mean Square 50.511 3.863 Sig Regression Residual Total 13.076 .000356b 274 275 a. Dependent Variable: Listens b. Predictors: (Constant), Gender

Answer 1

1. R^2 ( Coefficient of variation): It also known as the correlation coefficient it measure the correlation between the predicted value and actual value. It can be calculated using (Sum square due to regression / total sum of square)

Range of R^2 value is 0 to 1

the value near to 1 means your model is best

in our case the value of R^2 = 0.046

Means model is not best

2. Adj R^2 : The difference between R^2 and Adj R^2 is if no of variable increases in model then R^2 value increases but Adj R^2 is not effected by this so always give interpretation of model using the Adj R^2.

The value of Adj R^2 = 0.042

means model is not best

3. T test: The test in regression model is used to test the hypothesis coefficient b0 is 0 or not.

i.e. H0: b0 = 0

Test statistic of t-test is,

t = SSr / SSe

where SSr is sum of square due to regression

SSe is sum of square error

t = 50.511 / 1058.398

= 0.04773

4. Regression equation:

The general format of regression model is,

Y = b0 + b1 * X1

where, Y = Dependent variable = Listense

b0 = intercept = constant

b1 = regression coefficient = slope of line

X1 = Independent variable = Gender

Regression Equation,

Listense = constant + b1 * Gender

  

the coefficients table below ANOVA is missing from image take value of b0 and b1 from this table and put in above equation.

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