Exam 10: Multiple Regression

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What types of dependent variables are ok to use for linear regression?

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An analyst is interested in the relationship between number of cats a person has (an independent variable), number of dogs a person has (an independent variable) and the number of friends the person has (the dependent variable). She regresses number of FRIENDS on number of CATS and number of DOGS. The equation for the best-fitting straight line is FRIENDS = 10 − 2(CATS) + 1(DOGS) A) A person had 4 cats and 2 dogs. What is that person's predicted number of friends? B) What is the regression residual for a person with 0 cats, 0 dogs, and 0 friends?

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What proportion of the differences in the dependent variable is explained by the independent variables in the regression equation?  

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If you want to see which factor (age at marriage, educational level, or income) had the strongest net effect on marital happiness, what is an appropriate statistical technique to use?

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In the context of regression analysis, each of the following has at least one other name. State at least one of those other names:  

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If you want to see what the cases in your data set are like on a single continuous, interval/ratio variable, what is an appropriate statistical technique to use?

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The regression equation is Y = 50 - 5X1 + 10X2 - 20X3. A case has a value of 1 on X1, 2 on X2, and 3 on X3. What's the predicted value?

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Answer the questions that follow this SPSS output:   If the three variables in the correlation matrix were all used as independent variables in a single multiple regression analysis, would there be a multicollinearity problem? A) State yes or no. __________ B) Justify your answer by referring to one or more statistics in the matrix.

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According to the following regression equation: INCOME = 9000 + 2500(EDUC) − 100(AGE) − 5000(FEMALE), an increase of one year in education results in how much of a change in income? (State both the amount of change and the direction.)

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When would you use Crosstabs to look at the net effects of two independent variables on a dependent variable and when would you use Linear Regression?

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If you want to see the net effect of gender on academic achievement after controlling for age and parents' social class, what is an appropriate statistical technique to use?

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What is multicollinearity and why is it a problem?

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Let's say the correlation between SAT scores and college GPA is .70 but when you regress college GPA on SAT scores and parents' social class, the standardized coefficient for SAT scores is .02. What would this tell you?

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If you want to see how well percent of classes attended and percent of assigned reading completed do together in accounting for differences in student exam grades, what is an appropriate statistical technique to use?

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What kinds of questions can you answer using multiple regression?

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The regression equation is POVERTY = 10 + 1(UNEMPLOYMENT) - 0.5(COLLEGE). A county has a POVERTY rate of 30, an UNEMPLOYMENT rate of 10, and COLLEGE graduate rate of 10. What is the county's regression residual?

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What is a net effect?

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Answer the questions that follow this SPSS output:   The dependent variable is fallGPA (student's GPA after the fall semester). The independent variables are sizeHS (the size of their high school graduating class) and SAT (their best SAT score). A) What is the value of the multiple correlation (that is, the correlation between the dependent variable and the set of independent variables)? B) What is the value of the coefficient of determination? C) Of the two independent variables, which has the stronger net effect on the dependent variable? D) Write out the regression equation. (You may use Y and X's in the regression equation or, in place of the Y and X's, you may use variable names.)

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Which independent variable has the strongest net effect on GPA?  

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