Regression Analysis for Price and Sales

STATISTICS
[Document subtitle]
[DATE]

Assignment III
Question 3.1
Dependent variable: PRICE ($’000)
Independent variable: HOUSE (1000s of square feet), LOT (1000s of square feet), BED
(Number of bedrooms), BATH (Number of bathrooms), AGE (Age of the house in years)
PRICE=β0 + β1 HOUSE +β2 LOT +β3 BED+ β4 BATH + β5 AGE+ ε
(a) Regression output
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PRICE=217.218+ ( 23.667∗HOUSE ) + ( 18.065∗LOT ) + ( 20.350∗BED ) + ( 14.197∗BATH ) −(1.047∗AGE)+13
(b) Test to check whether the coefficients are significant or not
For variable: House
Null hypothesis H0 : β1=0 (Slope is insignificant)
Alternative hypothesis Ha : β2 ≠ 0 (Slope is significant)
Assuming significance level = 5%
The test statistics (t value) = 0.870
Corresponding (p value) =0.400
As the p value is higher than significance level and hence, null hypothesis would not be
rejected. Thus, it can be concluded that slope is insignificant and can be assumed zero.
For variable: LOT
Null hypothesis H0 : β2=0 (Slope is insignificant)
Alternative hypothesis Ha : β2 ≠ 0 (Slope is significant)
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Assuming significance level = 5%
The test statistics (t value) = 3.174
Corresponding (p value) =0.007
As the p value is lower than significance level and hence, null hypothesis would be rejected
and alternative hypothesis would be accepted. Thus, it can be concluded that slope is
significant and cannot be assumed zero.
For variable: BED
Null hypothesis H0 : β3=0 (Slope is insignificant)
Alternative hypothesis Ha : β3 ≠ 0 (Slope is significant)
Assuming significance level = 5%
The test statistics (t value) = 2.749
Corresponding (p value) =0.017
As the p value is lower than significance level and hence, null hypothesis would be rejected
and alternative hypothesis would be accepted. Thus, it can be concluded that slope is
significant and cannot be assumed zero.
For variable: BATH
Null hypothesis H0 : β4=0 (Slope is insignificant)
Alternative hypothesis Ha : β4 ≠0 (Slope is significant)
Assuming significance level = 5%
The test statistics (t value) = 1.503
Corresponding (p value) =0.157
As the p value is higher than significance level and hence, null hypothesis would not be
rejected and alternative hypothesis would not be accepted. Thus, it can be concluded that
slope is insignificant and can be assumed zero.
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