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Statistics: Regression Analysis Problems

1. The administrator of a school board in a large country was analyzing the average mathematics test scores in the schools under her control. She noticed that there were dramatic differences in scores among the schools. In an attempt to improve the scores of all the schools, she decided to determine the factors that account for the differences. Accordingly, she took a random sample of 40 schools across the country and, for each, determined the mean test score last year, the percentage of teachers in each school who hold at least one university degree in mathematics, the mean age, and the mean annual income (in $thousands) of mathematics teachers. Data is in file below. Use a 5% significance level
(a) Conduct a regression analysis to develop the equation.
(b) Is the model valid?
(c) Interpret and test the coefficients.
(d) Predict with 95% confidence the test score at a school where 50% of the mathematics teachers have mathematics degrees, the mean age is 43, and the mean annual income is $48,300.

2. A developer who specializes in summer cottage properties is considering purchasing a large tract of land adjoining a lake. The current owner of the tract has already subdivided the land into separate building lots and has prepared the lots by removing some of the trees. The developer wants to forecast the value of each lot. From previous experience she knows that the most important factors affecting the price of the lot are size, number of mature trees, and distance to the lake. From a nearby area, she gathers the relevant data for 60 recently sold lots. Data is in file below. Use a 5% significance level
a) Find the regression equation.
b) What is the standard error of estimate? Interpret its value.
c) What is the coefficient of determination? What does this statistic tell you?