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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LandSize
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Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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.