Question 4-16 Using the data in Problem 4-13, test to see if there is a statisti

Question

Question 4-16

Using the data in Problem 4-13, test to see if there is a statistically significant relationship between the grade on the first test and the final average at the 0.05 level of significance. Use the formulas in this chapter and Appendix D. Using computer software, find the least-squares regression for the data in problem 4-13. Based on the F test, is there a statistically significant relationship between the first test grade and the final average in the course? Steve Charles, a real estate appraiser in Lake Charles, Louisiana, has developed a regression model to appraise residential housing in the Lake Charles area. The model was developed using recently sold homes in a particular neighborhood. The price (Y) of the house is based on the square footage (X) of the house. The model is Y^= 33, 478 + 62.4 X The coefficient of correlation for the model is 0.63. (a) Use the model to predict the selling price of a house that is 1, 860 square feet. (b) A house with 1, 860 square feet recently sold for $165,000. Explain why this is not what the model predicted. (c) If you were going to use multiple regression to develop an appraisal model, what other quantitative variables might be included in the model? (d) What is the coefficient of determination for this model?

Explanation / Answer

Given model:

Y = 33478 + 62.4 X

Coefficient of correlation = 0.63

a) For X = 1860,

Y = 33478 + 62.4(1860)

Y = 149542

So,

According to the model,

Estimated selling price of a house having 1860 square feet will be $149,542.

b) Given that a house of 186- square feet is recently sold for $165,000 whereas in part a), our prediction was $149,542. This difference in because of the fact that square feet is not the only variable which can be used to predict the selling price of house. There can be many other variables related to the selling price. If the correlation between selling price and square feet would have been 1 then the model would have given the exact price of the house.

c) Some of the other factors for our multiple regression model can be:

--> Age of the property

--> Property rates (Generally varies according to location)

--> Vacancy Ratio

d) Coefficient of determination = (0.63)2 = 0.3969

This means that only 39.69% of the variation in selling price can be explained by the square foot. 60.31% variation in the selling price is due to other factors.

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