Find a best fit linear model for the given data. if needed, round to the nearest tenth. a) y=0.2x+3 b) y=4.3x-12.3 c) y=4.3x-12.9 d) y=4.3x+12.3

C) Y=4.3x-12.9

Step-by-step explanation:

You can tell by looking at the data that the choices B or C will be the best.

A graphing calculator or spreadsheet can give you the equation without a lot of fuss.

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Manual Calculation

The answer choices suggest the slope is 4.3, so you only need to find the means of x and y values to determine the y-intercept.

... mean(x) = (1+3+5+7+9)/5 = 5

... mean(y) = (-8+0+7+18+26)/5 = 8.6

Then the equation in point-slope form is ...

... y = 4.3(x -5) +8.6

Simplify to get slope-intercept form.

... y = 4.3x -12.9 . . . . . . . . matches selection C

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Slope calculation

The slope of the line of best fit is the ratio of the covariance of x and y to the variance of x. That is, the slope m is ...

... m = cov(x, y)/var(x) = (mean(xy)-mean(x)·mean(y))/(mean(x²)-mean(x)²)

Here, that is ...

... m = 43/10 = 4.3

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