Question

An agent for a real estate company in a large city would like to be able to predict the monthly rental cost for​ apartments, based on the size of the​ apartment, as defined by square footage. A sample of eight apartments in a neighborhood was​ selected, and the information gathered revealed the data shown below. For these​ data, the regression coefficients are b0= 181.5009 and b1 = 1.0277.

Monthly Rent ($)	Size (Square Feet)
925	800
1550	1300
800	900
1450	1200
1900	2000
925	650
1750	1350
1300	950

Determine the standard error of the​ estimate, SYX​, and interpret its meaning.

Answer 1

The second column (Y) is predicted by the first column (X). The slope and Y intercept of the regression line are 0.92865and -86.70793 respectively. The third column, (Y'), contains the predictions and is computed according to the formula:

Y' = 0.92865X - 86.70793

The fourth column (Y-Y') is the error of prediction. It is simply the difference between what a subject's actual score was (Y) and what the predicted score is (Y').

The sum of the errors of prediction is zero. The last column, (Y-Y')², contains the squared errors of prediction.