Answered: Calculate and give the value of the t…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

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)

-There appears to be a moderate positive linear relation between the two variables.

-There appears to be weak positive linear relation between the two variables.

-There appears to be no linear relation between the two variables

-There appears to be strong negative linear relation between the two variables.

-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)

-H₀: μ = 0, H₁: μ ≠ 0

-H₀: π = 0, H₁: π ≠ 0

-H₀: μ₁- μ₂= 0, H₁: μ₁- μ₂ ≠ 0

-H₀: β = 0, H₁: β ≠ 0

- How can you justify the assumption for this test? (Choose one from below)

-Since nπ and n(1-π) are both ≥5, the Central Limit Theorem applies and we can assume that p arises from a normal distribution

-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

-The boxplots indicate that the samples are fairly symmetric and the spreads are similar, so we can assume both sets of data come from normal distributions with the same spread

-The points are randomly scattered around a straight line, so the assumptions of linearity and constant spread are satisfied. The shape of the histogram indicates that the residuals come from a normal distribution

-None of these

-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)

184

182

Price vs Land Size
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Expert Solution

Step 1

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.