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Predicting GPA from ACT Scores using the Regression Equation

1. A government survey conducted to estimate the mean price of houses in a metropolitan area is designed to have a margin of error of $10,000. Pilot studies suggest that the population standard deviation is $70,000. Estimate the minimum sample size needed to estimate the population mean with the stated accuracy.

2. You are interested in finding out if a student's ACT score is a good predictor of their final college grade point average (GPA). You have obtained the following data and are going to conduct a regression analysis. Follow instructions on page 324 of your textbook under line of best fit to conduct this analysis?

22.0 3.0
32.0 3.78
33.0 3.68
21.0 2.94
27.0 3.38
25.0 3.21
30.0 3.65

a) What is the R? What type of relationship does it indicate (strong/weak; positive/negative)?

b) Go to the coefficients readout. The constant is the intercept. Under that is the ACT and that is the slope. Using the straight line formula of Y = mx + b, predict some future GPA scores: In the formula (m) is the slope; (x) is the variable that you are looking to use as a predictor; and (b) is the intercept. Predict GPA from the following ACT scores using the regression equation/straight line formula (show all your work):

1) 20
2) 25
3) 34

Solution Summary

This solution is comprised of detailed step-by-step calculations and analysis of the given problems and provides students with a clear perspective of the underlying concepts.