Is There an Association Between Spaces From Go and Property Cost?
Property
|
Spaces from GO
|
Cost
|
Residuals
|
Mediterranean Avenue
|
1
|
60
|
|
Baltic Avenue
|
3
|
60
|
|
Reading Railroad
|
5
|
200
|
|
Oriental Avenue
|
6
|
100
|
|
Vermont Avenue
|
8
|
100
|
|
Connecticut Avenue
|
9
|
120
|
|
St. Charles Place
|
11
|
140
|
|
Electric Company
|
12
|
150
|
|
States Avenue
|
13
|
140
|
|
Virginia Avenue
|
14
|
160
|
|
Penn Railroad
|
15
|
200
|
|
St. James Place
|
16
|
180
|
|
Tennessee Avenue
|
18
|
180
|
|
New York Avenue
|
19
|
200
|
|
Kentucky Avenue
|
21
|
220
|
|
Indiana Avenue
|
23
|
220
|
|
Illinois Avenue
|
24
|
240
|
|
B & O Railroad
|
25
|
200
|
|
Atlantic Avenue
|
26
|
260
|
|
Ventnor Avenue
|
27
|
260
|
|
Water Works
|
28
|
150
|
|
Marvin Gardens
|
29
|
280
|
|
Pacific Avenue
|
31
|
300
|
|
North Carolina Avenue
|
32
|
300
|
|
Pennsylvania Avenue
|
34
|
320
|
|
Short Line Railroad
|
35
|
200
|
|
Park Place
|
37
|
350
|
|
Boardwalk
|
39
|
400
|
|
Scatterplots,_Correlation,_and_Regression_-_Monopoly_Example'>AP Statistics - Chapter 3 - Scatterplots, Correlation, and Regression - Monopoly Example
Define the explanatory and response variables.
Draw a scatterplot of (Spaces From Go, Cost). Make the scatterplot reasonable size (not too small). Sketch the line of best fit.
Does there appear to be an association between the two variables?
Describe the data (association, form, strength, unusual features).
Find the Coefficient of Correlation, r. Describe what r means.
Find a “Line of Best Fit” by hand: y = mx+b.
The LSRL always goes through point ____________.
Find the LSQRL using your calculator.
Find the LSQRL using the Minitab Output for “Descriptive Statistics”
Find the LSQRL using the Minitab Output for “Regression Analysis”
What does b represent? What does m represent?
Are there any unusual points? What are they?
What is a residual? What is the formula for finding a residual?
Find the residuals. Create a residual plot. Comment on what you notice.
Is your model a good linear fit? Explain (use numerical and graphical summaries).
Find the standard deviation of the residuals. What does this mean?
Predict the cost of a “new property” that is 10 spaces from Go. Write a sentence describing your prediction.
Predict the cost of a “new property” that is 38 spaces from Go. Write a sentence describing your prediction.
Predict the cost of a “new” property that is 50 spaces from Go. Write a sentence describing your prediction.
Find r squared. Describe what it means.
Descriptive Statistics: Spaces From Go, Cost
Variable N N* Mean SE Mean StDev Minimum Q1 Median Q3
Spaces From Go 28 0 20.04 2.07 10.94 1.00 11.25 20.00 28.75
Cost 28 0 203.2 16.0 84.5 60.0 142.5 200.0 260.0
Variable Maximum
Spaces From Go 39.00
Cost 400.0
Regression Analysis: Cost versus Spaces From Go
The regression equation is
Cost = 67.3 + 6.78 Spaces From Go
Predictor Coef SE Coef T P
Constant 67.28 16.49 4.08 0.000
Spaces From Go 6.7845 0.7255 9.35 0.000
S = 41.2240 R-Sq = 77.1% R-Sq(adj) = 76.2%
Analysis of Variance
Source DF SS MS F P
Regression 1 148626 148626 87.46 0.000
Residual Error 26 44185 1699
Total 27 192811
Unusual Observations
Spaces
Obs From Go Cost Fit SE Fit Residual St Resid
3 5.0 200.00 101.21 13.40 98.79 2.53R
21 28.0 150.00 257.25 9.70 -107.25 -2.68R
26 35.0 200.00 304.74 13.36 -104.74 -2.69R
R denotes an observation with a large standardized residual.
Regression Analysis: Cost versus Spaces From Go – *** Removed Influential Points ***
The regression equation is
Cost = 43.2 + 8.24 Spaces From Go
Predictor Coef SE Coef T P
Constant 43.153 6.747 6.40 0.000
Spaces From Go 8.2377 0.3025 27.23 0.000
S = 15.7564 R-Sq = 97.0% R-Sq(adj) = 96.9%
Analysis of Variance
Source DF SS MS F P
Regression 1 184106 184106 741.57 0.000
Residual Error 23 5710 248
Total 24 189816
Unusual Observations
Spaces
Obs From Go Cost Fit SE Fit Residual St Resid
10 15.0 200.00 166.72 3.46 33.28 2.17R
17 25.0 200.00 249.10 3.53 -49.10 -3.20R
25 39.0 400.00 364.42 6.63 35.58 2.49R
R denotes an observation with a large standardized residual.
Scatterplots
Draw a scatterplot of (Spaces From Go, Cost).
Residual Plots
Create a residual plot with the monopoly data. Comment on what you see.
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