Answer:
y = 0.054x +8.018
Step-by-step explanation:
You want the least-squares regression line that fits the cost and miles data given.
The equation of the best-fit line is most easily calculated using a spreadsheet or statistics calculator. The display in the attachment shows the equation to be ...
y = 0.054x +8.018
If you want to calculate this "by hand", you need some statistics for the data. You need mean(x), variance(x), mean(y), and covariance(x, y).
µx = ∑x/n = 2193/7 ≈ 313.286
µy = ∑y/n = 174.45/7 ≈ 24.921
µx² = ∑x²/n = 689049/7 ≈ 98,435.571
µxy = ∑xy/n = 54761.33/7 ≈ 7823.047
The slope of the line of best fit is ...
m = cov(x, y)/var(x) = (µxy -µx·µy)/(µx² -(µx)²) ≈ 15.520/287.633 ≈ 0.054
Using the point-slope equation for the line with point (µx, µy), we have ...
y -24.921 = 0.054(x -313.286)
y = 0.054x +8.018
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Additional comment
To get the hand-calculated result to match the stat calculator result, the full precision of all intermediate values must be used. The calculation of variance and covariance involves finding the relatively small difference of large numbers, so is prone to significant error if there is any intermediate rounding. (The 3 dp numbers shown immediately above are insufficiently precise to match the result of the first section.)
