Question

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 7.0 9.0 11.0 11.5 12.5 12.0 Height, y 66.5 70.5 72.5 73.5 73.5 73.5 Find the regression equation. 9k+(D (Round to three decimal places as needed.) Choose the correct graph below. Ос. O A. O D. Ов. 75 75- 75- 75- Г 65- 65- 6 65- 6 65- 13 13 13 13 Shoe size Shoe size Shoe size Shoe size

Answer 1

x	y	x2	y2	xy
7	66.5	49	4422.25	465.5
9	70.5	81	4970.25	634.5
11	72.5	121	5256.25	797.5
11.5	73.5	132.25	5402.25	845.25
12	73.5	144	5402.25	882
12.5	73.5	156.25	5402.25	918.75
$\sum x=63$	$\sum y=430$	$\sum x^{2}=683.5$	$\sum y^{2}=30855.5$	$\sum xy=4543.5$

Slope :

$b=\frac{n(\sum xy)-(\sum x)(\sum y)}{n(\sum x^{2})-(\sum x)^{2}}$

$=\frac{6*4543.5-63*430}{6*683.5-(63)^{2}}$

= 1.295

$a=\frac{(\sum y)(\sum x^{2})-(\sum x)(\sum xy)}{n(\sum x^{2})-(\sum x)^{2}}$

  $=\frac{430*683.5-63*4543.5}{6*683.5-63^{2}}$

= 58.064

Hence the estimated regression equation is,

$\widehat{y}=58.064+1.295*x$

Scatter plot is given by,

Scatter plot 7 8 9 10 11 12 13

Correct option is c.