be a person\'s predicted G.P.A. if his/her mother had T2 years f eation? ur Inte
ID: 3365144 • Letter: B
Question
be a person's predicted G.P.A. if his/her mother had T2 years f eation? ur Interpret the following output. Variables are as follows: Years of schooling varies from 0 to 24 years Respondent's sex Respondent's race Verbal intelligence level varies from 0 to 10 points 1-male, 0-female 1-white, 0-nonwhite Variables Entered/Removed(b) Variables Removed Model Variables Entered Method Respondent's Sex, Respondent's Race, Verbal Intelligence Enter a All requested variables entered. b Dependent Variable: Years of schooling Model Summary Adjusted R Std. Error of the Model R Square Square Estimate 501(a) .251 250 2.5 a Predictors: (Constant), Respondent's Sex, Respondent's Race, Verbal Intelligence Coefficients(a) Unstandardized Coefficients Standardized Coefficients Model Si Std. Error 146 083 112 Beta (Constant) Respondent's Sex Respondent's Race 6.170 566 1.730 813 063 049 021 62.642 4.389 3.311 34.628 001 Verbal Intelligence .00 Dependent Variable: Years of schooling a. Interpret R, R2 and Standard error of estimate b. Write down the regression equation c. Interpret intercept d. Interpret B coefficients for sex, race and verbal intelligence e. What variable is the best predictor of educational attainment and why? f. Compute the educational attainment for a white woman whose verbal intelligence level equals 8.Explanation / Answer
a) Based on the table, the values for:
R = 0.501, R2 = 0.251, Std. error of estimate = 2.5
Interpretation: R-squared value (or) the co-efficient of multiple determination is a measure of how close the fitted data is to the actual data points. The quantum of it gives how much of variation in the dependent variable can be explained by the independent variables in the model. In this case, about 25% of variations in Years of schooling can be explained by Sex, Race and Verbal Intelligence.
Standard error of estimate is a measure to understand accuracy of predictions. It is the square root of the average squared error of the residuals (actual y - predicted y). A smaller value of the standard error indicates that the model's accuracy is better than one having a larger value of standard error.
b) Regression equation is : Years of School = 6.17 + (0.566*Sex) + (1.73*Race) + (0.813*Verbal Intelligence)
c) Intercept value is 6.17. This is the expected value of the dependent variables when all independent variables are Zero.
d) B Coefficients of Sex, Race and Verbal Intelligence are B1=0.566, B2=1.73 and B3=0.813 respectively.
e) To understand the best predictor, we must compare the standardized co-efficients because it removes any effect of the scale of each of the variables. The value of standardized co-efficient of a variable is the amount of standard deviations the dependent variable changes by for a unit change in the standard deviation of the variable in concern.
The variable with the highest magnitude of the standardized co-efficient is the best predictor of Years in School. In this case, standardized co-efficient magnitude of Sex, Race and Verbal Intelligence are 0.063, 0.049 & 0.021. This shows that Sex is the best predictor.
f) For the given scenario, Race = 1 (white), Sex = 0 (female) , Verbal Intelligence = 8.
Applying these values to the regression equation in b),
we see, Years in School = 6.17 + (0.566*0) + (1.73*1) + (0.813*8) = 6.17 + 1.73 + 6.504 = 14.4
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