STLRamsFan
May 5th, 2009, 11:29 AM
As some of you know, Math is my worst subject... So with that being said, here's an extra credit assignment I was just assigned and due tomorrow. Lets just say, I need a "little" bit of help with this:
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Many dependent variables in all areas of research serve as subjects of regression modeling. I list 4 such variables based on your major:
1. Grade point average of students who have completed on academic year at your college.
or
2 (made this up one up since I found it more interesting...). Goals scored by the Washington Capitals in the playoffs:
3, 0, 4, 1, 4, 5, 2, 3, 4
Total: 26
Average: 2.8
Choose one of these dependent variables or choose some other dependent variable for which you want to construct a prediction model. There may be a large number of independent variables that should be included in a prediction equation for the dependent variable you choose. List two potentially important independent variables x1 and x2 that you think might be (individually) strongly related to dependent variable. Next, obtain 10 data values each of which consists of a measure of your dependent variable Y and the corresponding values of x1 and x2.
1) Use the least squares formulas given in this chapter to fit two straight-line models –one for each independent variable- for predicting y.
2) Interpret the sign of the estimated slope in each case and use the t test to test B1=0. What assumptions must be satisfied to ensure the validity of these tests?
3) Calculate the coefficient of determination r- squares for each. Which of the independent variables predicts Y best for the 10 sampled sets of data? Is this variable necessarily best in general (that is, for the entire population)? Explain.
__________________________________________________ _
Many dependent variables in all areas of research serve as subjects of regression modeling. I list 4 such variables based on your major:
1. Grade point average of students who have completed on academic year at your college.
or
2 (made this up one up since I found it more interesting...). Goals scored by the Washington Capitals in the playoffs:
3, 0, 4, 1, 4, 5, 2, 3, 4
Total: 26
Average: 2.8
Choose one of these dependent variables or choose some other dependent variable for which you want to construct a prediction model. There may be a large number of independent variables that should be included in a prediction equation for the dependent variable you choose. List two potentially important independent variables x1 and x2 that you think might be (individually) strongly related to dependent variable. Next, obtain 10 data values each of which consists of a measure of your dependent variable Y and the corresponding values of x1 and x2.
1) Use the least squares formulas given in this chapter to fit two straight-line models –one for each independent variable- for predicting y.
2) Interpret the sign of the estimated slope in each case and use the t test to test B1=0. What assumptions must be satisfied to ensure the validity of these tests?
3) Calculate the coefficient of determination r- squares for each. Which of the independent variables predicts Y best for the 10 sampled sets of data? Is this variable necessarily best in general (that is, for the entire population)? Explain.