question archive A multiple linear regression model based on a sample of 30 homes is developed to predict appraised property value based on land area of the property and? age, in years
A multiple linear regression model based on a sample of 30 homes is developed to predict appraised property value based on land area of the property and? age, in years
Subject:StatisticsPrice:2.89 Bought3
A multiple linear regression model based on a sample of 30 homes is developed to predict appraised property value based on land area of the property and? age, in years. The SSR is 13,705 and the SSE is 85,221.
Hypotheses to test are as follows:
H0: B1 = B2 =0
H1: At least one Bj not equal 0, j=1,2
a. What is the test statistic and the P value?
b. Compute the coefficient of multiple determination r2 and interpret its meaning
The coefficient of multiple determination indicates that ___% of the variation in ____ can be explained by the variation in ____
Compute the adjusted r2 (round to four decimal places as needed)
Purchase A New Answer
Custom new solution created by our subject matter experts
GET A QUOTE
Answer Preview
a) Given that,
SSR =13705 , SSE =85221
Degree of freedom for Regression = 3-1=2
Degree of freedom for Error= 30-3=27
Since, test statistic(F) =?MSEMSR?=85221/2713705/2?=2.171?
P-value =0.1336
( i have used excel command "=FDIST(x,df1,df2)" Here x=2.171,df1=2,df2=27)
b) ?R2=SSTSSR??
Since, SST = SSR+SSE=13705+85221=98926
Thus, ?R2=9892613705?? =0.1385
The coefficient of multiple determination indicates that 13.85% of the variation in dependent variable can be explained by the variation in Independent variable.
c) Formula for Adjusted R-square is ---
SSE=85221
?Radj2?=1−[n−k−1(1−R2)(n−1)?]?
Using ?R2? =0.1385,n=30,k=2 then
?Radj2?=0.0747?
