Question
I need some assistance with these 3 questions Find the equation of the least-squares line (i.e. fill in the numbers for =+y^=a+bx), where y is
I need some assistance with these 3 questions
- Find the equation of the least-squares line (i.e. fill in the numbers for =+y^=a+bx), where y is price and x is mileage.
- Find & practically interpret the slope (b)
- Find & interpret the y-intercept (a) if an interpretation is possible. If it's not possible, just report the y-intercept and explain whyit can not be interpreted practically
These the data I have so far
Simple linear regression results:
Dependent Variable: Price Independent Variable: Mileage Price = 41116.768 - 0.17675013 Mileage Sample size: 30 R (correlation coefficient) = -0.46576164 R-sq = 0.2169339 Estimate of error standard deviation: 9248.6584
Parameter estimates:
Parameter | Estimate | Std. Err. | Alternative | DF | T-Stat | P-value |
---|---|---|---|---|---|---|
Intercept | 41116.768 | 2661.5978 | 0 | 28 | 15.448152 | <0.0001 |
Slope | -0.17675013 | 0.06346236 | 0 | 28 | -2.7851175 | 0.0095 |
Analysis of variance table for regression model:
Source | DF | SS | MS | F-stat | P-value |
---|---|---|---|---|---|
Model | 1 | 6.6350549e8 | 6.6350549e8 | 7.7568794 | 0.0095 |
Error | 28 | 2.3950551e9 | 85537682 | ||
Total | 29 | 3.0585606e9 |
Price | Mileage |
28900 | 28330 |
41000 | 21650 |
41499 | 24376 |
38999 | 4644 |
25383 | 24053 |
43499 | 4863 |
34980 | 6432 |
61829 | 10643 |
39499 | 82140 |
28691 | 40210 |
39502 | 59130 |
28998 | 30000 |
42094 | 10762 |
30749 | 41148 |
41000 | 21650 |
24795 | 91785 |
26500 | 19971 |
45590 | 4220 |
43343 | 8324 |
30975 | 24909 |
19500 | 101449 |
25995 | 51195 |
28500 | 39942 |
35999 | 34883 |
22997 | 23005 |
33499 | 11342 |
27499 | 33706 |
33975 | 17546 |
31313 | 86891 |
64499 | 13372 |
- Find & practically interpret the correlation coefficient (r)
Correlation coefficient r =Cov(X, Y)/ XY
sigma Y | sigma X |
10097.13 | 26607.37 |
Cov (X, Y) = -125130598.4
Thus, r = -125130598.4 / 268658017.7
r = -0.4657
Interpretation:
Price (Y) and Mileage(X) are negatively correlated to each other. The strength of correlation is weak. In other words, the correlation between mileage and price is -0.46576. This means that they have a medium negative correlation, so that if we increase mileage, the price decreases.
- Find & practically interpret the coefficient of determination (R2)
= r * r
= (-0.4657) * (- 0.4657)
=0.2169
Interpretation:
The value of the R2(R Square) is 0.216934. This means that 21.6934% of the variability in price can be explained by mileage.
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