Question

9.3.32 Question Help Find the equation of the regression line for the given data. Then construct a scatter plot of the data and draw the regression line. The table shows the shoe size and heights (in.) for 6 men. Shoe size, X 6.0 8.5 11.0 120 12.5 13.5 Helghty 65.0 68.0 69.0 720 72.0 73.0 Find the regression equation (Round to three decimal places as needed.)

Answer 1

To calculate the equation of regression we need to do the following table calculation as:

X Y X*Y x2 Y2 6 65 390 36 4225 8.5 68 578 72.25 4624 11 69 759 121 4761 12 72 864 144 5184 12.5 72 900 156.25 5184 13.5 73 985.5 182.25 5329 Sum = 63.5 419 4476.5 711.75 29307

The average of both variable is calculated as:

η X ΙΣΧ 63.5 6 10.583333333333 η 1=1

Y ΣΥ 419 6 69.833333333333 η i=1

Now the sum of squares is calculated as:

2 12 SSxx = ΣΧ? (Σ 711.75 – 63.5? 6 = 39.708333333333 n i=1 1=1

SSyy = ΣΥ? - 29307 – 419? /6 = 46.833333333336

2 η SSxy = ΣΧΥ, X, ΣΥ; 4476.5 – 63.5 x 419/6 = 42.083333333334 n i=1 1=1

Now the slope and the intercept for regression equation is calculated as:

m = SSXY SSxx 42.083333333334 39.708333333333 - 1.0598

n = Y - X - m = ᏮᏭ.833333333333 - 10.583333333333 x1.05Ꮽ8 = 58.617

Now the regression equation is calculated as:

$\hat{Y}=1.060X+ 58.617$

The scatterplot and the regreesion line is plotted as: