Treadmills Case: Consumer Reports provided extensive testing and ratings for 24

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

Using Excel Megastat output, report multiple regression equation for predicting the price of treadmills when knowing their overall score and quality rating.

Interpret the meaning of each of the regression coefficient starting with b0 as an estimate of 0, and continuing with b1, b2…. For each “bn” report a value and which “X” is it a coefficient for.

Partial regression coefficient for the y-intercept, b0 = _______
Interpretation of b0 –

       Does the interpretation of the y-intercept make sense? Why yes/no?

Partial regression coefficient for X1 (score in points), b1 = ________
Interpretation of b1 –

…Continue in the same fashion until you have interpreted all partial regression coefficients.

Explanation / Answer

We are assigning the quality rating 0f 3 to excellent, 2 to very good and 1 to good and we are getting the below equation when regressing quality_rating and score on price

y=-2372.268+65.43(score)-390(quality_rating)

This means that with every increase of 1 unit in score, price would go up by 65.43. With every increase of 1 in quality rating, price would go down by 390. Since, we have assigned three categories of quality rating, if excellent(1), it would go down by 390, if very good (2), it would go down by 780 and if good (3), it would go down by 1170.

Here, we are getting the p-value greater than 0.05 for all the variables. Hence, none of the variables are significant.

SUMMARY OUTPUT Regression Statistics Multiple R 0.695151304 R Square 0.483235336 Adjusted R Square 0.434019653 Standard Error 643.3456574 Observations 24 ANOVA df SS MS F Significance F Regression 2 8127816.999 4063908.5 9.818726737 0.00097628 Residual 21 8691766.334 413893.6349 Total 23 16819583.33 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept -2372.268014 3009.616044 -0.788229455 0.439370216 -8631.107205 3886.571178 -8631.107205 3886.571178 Score 65.4298905 33.47382766 1.954658163 0.064066339 -4.182744942 135.0425259 -4.182744942 135.0425259 Quality_Rating -390.0062846 311.0593661 -1.253800165 0.223693328 -1036.889649 256.8770797 -1036.889649 256.8770797

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.