Treadmills Case: Consumer Reports provided extensive testing and ratings for 24
ID: 3232479 • Letter: T
Question
Treadmills Case:
Consumer Reports provided extensive testing and ratings for 24 treadmills. An overall score, based primarily on ease of use, ergonomics, exercise range, and quality, was developed for each treadmill tested. In general, a higher overall score indicates better performance. The following data (Excel file available in Connect “Lab assignment 5” folder) contains data on the price, overall score, and quality rating for the 24 treadmills (Consumer Reports, February 2006).
Use the “good” quality rating as the base when creating the dummy variables for quality.
Brand & Model
Price ($)
Score (points)
Quality
Landice L7
2900
86
Excellent
NordicTrack S3000
3500
85
Very good
SportsArt 3110
2900
82
Excellent
Precor
3500
81
Excellent
True Z4 HRC
2300
81
Excellent
Vision Fitness T9500
2000
81
Excellent
Precor M 9.31
3000
79
Excellent
Vision Fitness T9200
1300
78
Very good
Star Trac TR901
3200
72
Very good
Trimline T350HR
1600
72
Very good
Schwinn 820p
1300
69
Very good
Bowflex 7-Series
1500
83
Excellent
NordicTrack S1900
2600
83
Very good
Horizon Fitness PST8
1600
82
Very good
Horizon Fitness 5.2T
1800
80
Very good
Evo by Smooth Fitness FX30
1700
75
Very good
ProForm 1000S
1600
75
Very good
Horizon Fitness CST4.5
1000
74
Very good
Keys Fitness 320t
1200
73
Very good
Smooth Fitness 7.1HR Pro
1600
73
Very good
NordicTrack C2300
1000
70
Good
Spirit Inspire
1400
70
Very good
ProForm 750
1000
67
Good
Image 19.0 R
600
66
Good
Test the significance of the overall regression model at = .01. Use the 7-step hypothesis test and either of the two approaches.
Report the value of the multiple coefficient of determination and interpret its meaning.
Test the partial regression coefficient for the variable “score”. Is the coefficient significant at = 0.1? (p-value approach hypothesis test)
Test the partial regression coefficient for the first dummy variable (2). Is the coefficient significant at = 0.1? (p-value approach hypothesis test)
Report a 95% interval for the mean value of all treadmills that are in “good” condition and have a score of 79. Interpret the meaning of the interval in the context of the problem.
Report a 95% interval for an individual value of y when the mean value of all treadmills that are in “good” condition and have a score of 79. Interpret the meaning of the interval in the context of the problem.
Analyze the correlation matrix, do you see any multicollinearity in the model? Comment on which variables appear to be problematic?
Brand & Model
Price ($)
Score (points)
Quality
Landice L7
2900
86
Excellent
NordicTrack S3000
3500
85
Very good
SportsArt 3110
2900
82
Excellent
Precor
3500
81
Excellent
True Z4 HRC
2300
81
Excellent
Vision Fitness T9500
2000
81
Excellent
Precor M 9.31
3000
79
Excellent
Vision Fitness T9200
1300
78
Very good
Star Trac TR901
3200
72
Very good
Trimline T350HR
1600
72
Very good
Schwinn 820p
1300
69
Very good
Bowflex 7-Series
1500
83
Excellent
NordicTrack S1900
2600
83
Very good
Horizon Fitness PST8
1600
82
Very good
Horizon Fitness 5.2T
1800
80
Very good
Evo by Smooth Fitness FX30
1700
75
Very good
ProForm 1000S
1600
75
Very good
Horizon Fitness CST4.5
1000
74
Very good
Keys Fitness 320t
1200
73
Very good
Smooth Fitness 7.1HR Pro
1600
73
Very good
NordicTrack C2300
1000
70
Good
Spirit Inspire
1400
70
Very good
ProForm 750
1000
67
Good
Image 19.0 R
600
66
Good
Explanation / Answer
Consumer Reports provided extensive testing and ratings for 24 treadmills. An overall score, based primarily on ease of use, ergonomics, exercise range, and quality, was developed for each treadmill tested. In general, a higher overall score indicates better performance. The following data (Excel file available in Connect “Lab assignment 5” folder) contains data on the price, overall score, and quality rating for the 24 treadmills (Consumer Reports, February 2006).
Use the “good” quality rating as the base when creating the dummy variables for quality.
Here dependent variable is price and there are two independent variables as score and quality.
Here there are two independent variables so we use multiple regression.
We can do multiple regression in MINITAB.
steps :
ENTER data into MINITAB sheet --> STAT --> Regression --> Regression --> Response : price --> Predictors : score and quality --> Results : select second option --> ok --> ok
————— 5/5/2017 8:18:57 PM ————————————————————
Welcome to Minitab, press F1 for help.
Regression Analysis: Price ($) versus Score (points), Quality
The regression equation is
Price ($) = - 3932 + 65.4 Score (points) + 390 Quality
Predictor Coef SE Coef T P
Constant -3932 2120 -1.85 0.078
Score (points) 65.43 33.47 1.95 0.064
Quality 390.0 311.1 1.25 0.224
S = 643.346 R-Sq = 48.3% R-Sq(adj) = 43.4%
Analysis of Variance
Source DF SS MS F P
Regression 2 8127817 4063908 9.82 0.001
Residual Error 21 8691766 413894
Total 23 16819583
Test the significance of the overall regression model at = .01. Use the 7-step hypothesis test and either of the two approaches.
Here we have to test the hypothesis that,
H0 : Bj = 0 Vs H1 : Atleast one of the Bj is differ than 0.
Assume alpha = level of significance = 0.01
Here test statistic follows F-distribution.
Test statistic = 9.82
P-value = 0.001
P-value < alpha
Reject H0 at 0.01 significance level.
COnclusion : Atleast one of the Bj is differ than 0.
Here we get significant result about overall significance.
Report the value of the multiple coefficient of determination and interpret its meaning.
multiple coefficient of determination is denoted by R2.
R2 = 48.3% = 0.483
It expresses proportion of variation in price which is explained by score and quality.
Test the partial regression coefficient for the variable “score”. Is the coefficient significant at = 0.1? (p-value approach hypothesis test)
Here we have to test the hypothesis that,
H0 : B = 0 Vs H1 : B not= 0
where B is population slope for score.
Assume alpha = 0.1
Here test statistic follows t-distribution.
Test statistic = 1.95
P-value = 0.064
Here P-value < alpha
Reject H0 at 0.1 significance level.
Conclusion : The population slope for score is differ than 0.
Here we get significant result about score.
Test the partial regression coefficient for the first dummy variable (2). Is the coefficient significant at = 0.1? (p-value approach hypothesis test)
Here we have to test
H0 : B = 0 Vs H1 : B not= 0
where B is population slope for quality.
Assume alpha = 0.1
t = 1.25
P-value = 0.224
P-value > alpha
Accept H0 at 0.1 significance level.
Conclusion : The population slope for quality is 0.
We get insignificant result about quality.
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