The following alternative hypotheses were tested:
Alternative hypotheses
There is a statistically significant relationship between sales price and a home’s value.
There is a statistically significant relationship between total rooms and a home’s value.
There is a statistically significant relationship between bathrooms and a home’s value.
There is a statistically significant relationship between bedrooms and a home’s value.
There is a statistically significant relationship between age house and a home’s value.
Null hypotheses
The following null hypotheses were tested:
There is no statistically significant relationship between sales price and a home’s value.
There is no statistically significant relationship between total rooms and a home’s value.
There is no statistically significant relationship between bathrooms and a home’s value.
There is no statistically significant relationship between bedrooms and a home’s value.
There is no statistically significant relationship between age house and a home’s value.
Step 1
The multiple linear regression model for the study is specified as
("Hypothesis Testing - Statistics How To", 2018).
Y = β o + β 1 X1 + β 2 X2 +β 3 X3 +β 4 X 4 +β 5 X 5 + €
Where y i is a home’s value.
β 0 is a constant
β 1 x 1 is sales price
β 2 x 2 is total rooms
β 3 x 3 is bathrooms
β 4 x 4 is bedrooms
β 5 X 5 is age house
€ = error term
Step 2
Histogram
Scatter plot
Step 3
Mean
| Descriptive Statistics | |||
|
Mean |
Std. Deviation |
N |
|
| air-condition |
.09 |
.286 |
888 |
| sales price |
159022.11 |
74581.375 |
888 |
| total rooms |
6.17 |
1.447 |
888 |
| bathrooms |
1.83 |
.806 |
888 |
| bedrooms |
2.98 |
.804 |
888 |
| age house |
62.51 |
36.399 |
888 |
Step 4 .
The regression equation will, therefore, be specified as:
y i = - -.024 + 3.65 x 1 +0.011 x 2 +. 080 x 3 + -0.012 x 4 ............. -.002 x 5
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Tables
Model Summary b |
|||||||||||||||
| Model |
R |
R Square |
Adjusted R Square |
Standard error of the Estimate |
Change Statistics |
||||||||||
R Square Change |
F Change |
df1 |
df2 |
Sig. F Change |
|||||||||||
| 1 |
.435 a |
.189 |
.184 |
.259 |
.189 |
41.114 |
5 |
882 |
.000 |
||||||
| a. Predictors: (Constant), age house, bedrooms, sales price, bathrooms, total rooms | |||||||||||||||
| b. Dependent Variable: air-condition | |||||||||||||||
|
ANOVA |
|||||||||||
| Model |
Sum of Squares |
df |
Mean Square |
F |
Sig. |
||||||
| 1 | Regression |
13.759 |
5 |
2.752 |
41.114 |
.000 b |
|||||
| Residual |
59.034 |
882 |
.067 |
||||||||
| Total |
72.793 |
887 |
|||||||||
| a. Dependent Variable: air-condition ("ANOVA - Statistical Test - The Analysis Of Variance", 2018) | |||||||||||
| b. Predictors: (Constant), age house, bedrooms, sales price, bathrooms, total rooms | |||||||||||
|
Coefficients |
|||||||||||||||||
| Model |
Unstandardized Coefficients |
Standardized Coefficients |
t |
Sig. |
95.0% Confidence Interval for B |
||||||||||||
|
B |
Std. Error |
Beta |
Lower Bound |
Upper Bound |
|||||||||||||
| 1 | (Constant) |
-.024 |
.040 |
-.615 |
.539 |
-.102 |
.053 |
||||||||||
| sales price |
3.652E-007 |
.000 |
.095 |
2.579 |
.010 |
.000 |
.000 |
||||||||||
| total rooms |
.011 |
.011 |
.053 |
.959 |
.338 |
-.011 |
.032 |
||||||||||
| bathrooms |
.080 |
.015 |
.224 |
5.272 |
.000 |
.050 |
.109 |
||||||||||
| bedrooms |
-.012 |
.018 |
-.032 |
-.657 |
.512 |
-.046 |
.023 |
||||||||||
| age house |
-.002 |
.000 |
-.245 |
-6.684 |
.000 |
-.002 |
-.001 |
||||||||||
| a. Dependent Variable: air-condition | |||||||||||||||||
|
Residuals Statistics |
|||||
|
Minimum |
Maximum |
Mean |
Std. Deviation |
N |
|
| Predicted Value |
-.28 |
.73 |
.09 |
.125 |
888 |
| Residual |
-.729 |
1.138 |
.000 |
.258 |
888 |
| Std. Predicted Value |
-2.947 |
5.130 |
.000 |
1.000 |
888 |
| Std. Residual |
-2.818 |
4.398 |
.000 |
.997 |
888 |
| a. Dependent Variable: air-condition | |||||
3. Third .
According to the Model summary and ANOVA table, all the Four variables have a statistically significant relationship thus influencing a home’s value since the p<0.05.
References
ANOVA - Statistical Test - The Analysis Of Variance. (2018). Retrieved from https://explorable.com/anova
Hypothesis Testing - Statistics How To. (2018). Retrieved from https://www.statisticshowto.datasciencecentral.com/probability-and-statistics/hypothesis-testing/
Tarlow, K. (2015). Teaching principles of inference with ANOVA. Teaching Statistics, 38(1), 16-21. doi: 10.1111/test.12085
Understanding Descriptive and Inferential Statistics. (2018). Retrieved from https://statistics.laerd.com/statistical-guides/descriptive-inferential-statistics.php
