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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

  1. 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.
  2. Find & practically interpret the slope (b)
  3. 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
  1. 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.

  1. 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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