The accompanying data are the shoe sizes and heights (in inches) of 14 men. Find the equation of the regression line. Then construct a scatter plot of the data and draw the regression line. Then use the regression equation to predict the value of y for each of the given x-values, if meaningful. If the x-value is not meaningful to predict the value of y, explain why not. (a) x= 11.5
(b) x= 8.0
(c) x = 15.5
(d) x = 10.0

Complete question :

Data of shoe sizes :

X:

8.5

9.0

9.0

9.5

10.0

10.0

10.5

10.5

11.0

11.0

11.0

12.0

12.0

12.5

Height (y) :

66.5

68.5

67.5

70.0

70.0

72.0

71.5

70.0

71.0

71.5

73.0

73.5

74.0

74.0

Kindly check explanation

Step-by-step explanation:

Using the online regression calculator :

The regression model obtained in the form:

ŷ = mx + c is ;

ŷ = 1.792X + 52.176

Where ŷ is the predicted or dependent variable

m = 1.792 is the gradient or slope of the regression line

x = the independent variable

c = 52.176 = intercept, where the line of best fit intersects the y axis.

Given the following x values, predict ŷ

(a) x= 11.5

ŷ = 1.792(11.5) + 52.176 = 72.784

(b) x= 8.0

ŷ = 1.792(8.0) + 52.176 = 72.784 = 66.512

(c) x = 15.5

ŷ = 1.792(15.5) + 52.176 = 79.952

(d) x = 10.0

ŷ = 1.792(10.0) + 52.176 = 70.096

The predicted values are meaningful as they show are very close to the actual values of height (y). This could be attributed to the high correlation Coefficient of 0.9299 which exists between both variables