Related questions
Part A
The next questions are in relation to recent study of house prices in Sydney. The variables investigated are:
1 SalePrice Selling Price in Thousands of dollars
2 Distance Distance from Sydney CBD in Kilometers
3 LandSize Land size in square meters
4 Building Area Building Area Construction in square meters
Research Question: Is there a relation between Price of the house and land size?
The output below presents the relation between Price of the house (in thousands of dollars) and land size.The
>results1 <- lm(SalePrice ~ LandSize)
>results1
Call: lm(formula = SalePrice ~ LandSize)
Coefficients:
(Intercept) LandSize
493.4233 1.5821
>summary(results1)
Call: lm(formula = SalePrice ~ LandSize)
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 493.42 119.47 4.13 0.0001
LandSize 1.5821 0.1926 **** *****
Residual standard error: 483.86 on 182 degrees of freedom
Multiple R-squared: 0.52, Adjusted R-squared: 0.2665
- Comment on the relation between the two test marks using the scatterplot.(Choose one from below)
-If the linear equation between the Sale Price and Land Sale is given as:
What is the value of a from the output above (2 dp)
=
What is the value of b from the output above (2 dp)
=
Is there a relation between Sale Price and Land Size?
Perform an appropriate hypothesis test to answer the above research question:
- The null and alternative hypotheses are (Choose one from below)
.
- How can you justify the assumption for this test? (Choose one from below)
-Calculate and give the value of the t test statistic? (3 dp): (Choose one from below)
| 205.9 | 0.193 | 8.215 | 4.130 | 4.224 |
- What are the degrees of freedom? (Choose one from below)
| 46 | 184 | 50 | 26 | 182 |
1) From the scatter plot, there appears to be a moderate positive linear relation between the two variables.
2) a=493.42 and b=1.58
3) H0: β = 0, H1: β ≠ 0
4) The shape of the histogram indicates that the scores may be from a normal distribution and/or the sample size is reasonably large so the sample mean will be from a normal population.
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