Coefficient of Correlation and Determination
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A sample of 12 homes sold in St.Paul, Minnesota, is selected. Can we conclude that as the size of the home (reported below in thousands of square feet) increases, the selling price (reported in $ thousands) also increases? Use the MegaStat Scatterplot function in Regression or the Excel Chart Wizard to create a scatter plot, and answer b) through d) below. Then, conduct a regression analysis and answer e), f), and g)
a.
Place scatter plot below, with a title:
(do not connect the dots, but show a "line of best fit")
b) Does the relationship appear to be a positive or a negative relationship?
c) The independent variable is:
d) The dependent variable is:
(which is dependent on the other?
Home Size (thousands of sq.ft) Selling Price($ thousands)
1.4 100
1.3 110
1.2 105
1.1 120
1.4 80
1.0 105
1.3 110
0.8 85
1.2 105
0.9 75
1.1 70
1.1 95
Use the Analysis ToolPak or Megastat to conduct a regression analysis,
and paste the output below:
e) Identify the coefficient of correlation
f) Identify the coefficient of determination
g) Can we conclude that there is a significant positive association
between the size of the home and the selling price? Use the .05
significance level.
Yes or No?
Why?
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Solution Summary
This Solution contains calculations and graphical representations to aid you in understanding the Solution to this question.
Education
- BSc , Wuhan Univ. China
- MA, Shandong Univ.
Recent Feedback
- "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
- "excellent work"
- "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
- "Thank you"
- "Thank you very much for your valuable time and assistance!"
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