A realty company would like to develop a regression model to help it set weekly

Question

A realty company would like to develop a regression model to help it set weekly rental rates for beach properties (y). The independent variables for this model are the number of bedrooms a property has   x1 , its age x2 , and the number of blocks away from the ocean it isx3. Use the accompanying data to complete parts a through e below.

a) Construct a regression model using all three independent variables.

b) Test the significance of each independent variable using = 0.100.

c) Construct and interpret a 90 % confidence interval for the regression coefficient for the Bedroom variable in terms of the expected rental rate.

Rental ($) Bedrooms Age Blocks 1000 2 14 4 1100 3 8 2.5 1600 3 8 3 2300 3 18 2.5 2800 4 12 2.5 3200 5 13 2 3600 4 6 2.5 4600 6 5 1.5 6500 5 17 1 7800 5 7 0.5

Explanation / Answer

Sol:

regmod1 <- lm(Hosuerent$`Rental _$_`~.,data=Hosuerent)

coefficients(regmod1)
(Intercept) Bedrooms Age Blocks
7742.18645 22.40552 14.69438 -2063.86721
>

regression eq is

rental=7742.18645 +22.40552 (Bedrooms )+14.69438 (Age )-2063.86721 (Blocks )

Solutionb:

summary(regmod1)

Coefficients:
Estimate Std. Error t value Pr(>|t|)  
(Intercept) 7742.19 3930.27 1.970 0.0964 .
Bedrooms 22.41 561.63 0.040 0.9695  
Age 14.69 82.52 0.178 0.8645  
Blocks -2063.87 674.97 -3.058 0.0223 *

For Bedrooms p=0.9695  

alpha=0.1

p>alpha

Bedrooms variable is not significant

for age variable

p=0.8645

p>0.1

age is not significant variable

for blocks

p=0.0223

p<0.1

blocks variable is significant.

Solutionc:

rcode is

confint(regmod1, level=0.90)
5 % 95 %
(Intercept) 104.9616 15379.4113
Bedrooms -1068.9486 1113.7597
Age -145.6597 175.0484
Blocks -3375.4589 -752.2756

for bedrooms 90% confidence interval for the regression coefficient are

-1068.9486 and 1113.7597 holding other variables constant.

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