show work please thank you Steve Caples a real estate apprai

show work please thank you

Steve Caples, a real estate appraiser in Lake Charles, Louisiana, has developed a regression model to help 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 Hat Y = 13,473 + 37.65X 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 $95,000. Explain why this is not what the model predicted.

Solution

Given that Y = 13,473+37.65 x

a) When x = 1860 sq ft, Y = 13473+37.65(1860)

= 83502

----------------------------

b) A house actually areaed 1860 sqft sold for 95000 i.e. 95000-83502 more

Actually, line of best fit is not the exact predictor but it is line which has the least deviations from the actual

A scatter plot is plotted and if linear trend is detected a line which lies nearest to all the dots is drawn.

ACtual slope and intercept is calcualted using least squares method i.e. the square of distances of actual from predicted remains the minimum

Hence actual price though exactly does not equal in the long run for the prices in the range this line may serve as a predictor for valuations with minimum deviations.