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=  328.6794 and b1=0.8881. Complete parts​ (a) through​ (d).

Monthly Rent ($)	Size (Square Feet)
925	750
1,500	1,250
850	900
1,450	1,250
1,950	2,000
950	650
1,825	1,300
1,350	1,100

1. Determine the coefficient of​ determination, r² ​, and interpret its meaning. (round to three decimals)

2. Determine the standard error of the​ estimate, S_YX (round to three decimals)

3. What is the meaning of SYX?

1. SYX measures the typical difference between an​ apartment's actual rent and the rent predicted by the regression equation.

2. SYX measures the typical difference between an​ apartment's size and the size predicted by the regression equation.

3. SYX measures the amount by which an​ apartment's rent is greater than the rent predicted by the regression equation.

4. SYX measures the amount by which an​ apartment's rent is less than the rent predicted by the regression equation.

Answer 1

Using Excel, go to Data, select Data Analysis, choose Regression. Put Monthly Rent in Y input range and Size in X input range.

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.900
R Square	0.809
Adjusted R Square	0.777
Standard Error	196.097
Observations	8
ANOVA
	df	SS	MS	F	Significance F
Regression	1	978025.454	978025.454	25.434	0.002
Residual	6	230724.546	38454.091
Total	7	1208750.000
	Coefficients	Standard Error	t Stat	P-value
Intercept	328.679	214.054	1.535	0.176
Size	0.888	0.176	5.043	0.002

Coefficient of determination (R-square) = 0.809

Standard error of the​ estimate = 196.07

SYX measures the typical difference between an​ apartment's actual rent and the rent predicted by the regression equation. (Option 1)