Suppose that a simple linear regression model is appropriate for describing the

Question

Suppose that a simple linear regression model is appropriate for describing the relationship between y = house price and x = house size (sq ft) for houses in a large city. The true regression line is y = 24,000 + 45x and sigma = 4000 What is the average change in price associated with one extra sq ft of space? $________ With an additional 100 sq ft of space? $________ What proportion of 1900 sq ft homes would be priced over $110,000? (Round your answer to four decimal places.) _____________ Under $100,000 (Round your answer to four decimal places.) ___________ You may need to use the appropriate table in Appendix A to answer this question. The accompanying summary quantities resulted from a study in which X was the number of photocopy machines serviced during a routine service call and y was the total service time (min). n = 15 sigma (y - y^bar)^2 = 22, 398.08 sigma (y-y^circ)^2 = 2613.51 What proportion of observed variation in total service time can be explained by a linear probabilistic relationship between total service time and the number of machines serviced? (Give the answer to three decimal places.) 0.116

Explanation / Answer

Given:

Total Sum of Squares, TSS = 22398.08

Residual sum of squares, RSS = 2613.51

Using the relation:

R2 = 1-(RSS/TSS) = 1-(2613.51/22398.08) = 0.8833 = 88.33 %

Thus, % of variability in Y explained by the linear relationship b/w X and Y is equal to 88.33%

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