Question

Here are the height and shoe-size information from our class survey at the beginning of the quarter.

Height (in inches)	Shoe Size (US Womens)
66	10.5
64	7
67	7.5
65	7.5
64	9
68	7.5
74	14.5
67	9
72	11.5
66	7.5
64	7.5
65	8.5
72	13.5
63	8
66	8
60	8
67	7.5

I converted all our measurements so they were in the same units.   Use technology to analyze these data as in Chapters 6,7, and 8. Use height as your explanatory variable and shoe size as your response variable.

1. Describe your scatterplot (you don’t have to turn in your actual plot). (Form, direction, strength, outliers?)
2. Write the equation of the regression line for predicting shoe size from height.
3. Write the correlation.
4. Write a sentence or two commenting on the appropriateness of the linear model.
5. Use your answer from b. to predict the shoe size of a person who is 61 inches tall.
6. I am 61 inches tall, and my shoe size is US Womens 7. What is my residual?

Answer 1

a)

b)

We will be applying the Linear regression model here, it can be done by using the function =LINEST(y_value, x_value, TRUE, TRUE) where y_values contain values of Shoe size here and x_values have height values.

Select 5 rows and 2 columns and then write the formula in the first cell and after that, press Shift + Ctrl + Enter.    

The equation comes out to be -

Shoe size = -23.97 + 0.49*Height

c)

The correlation coefficient comes out to be 0.781.

d)

From the scatterplot, we can see that the two variables are linearly correlated. Here, linear regression can be applied as it is appropriate.

e)

Shoe size = -23.97 + 0.49*Height

When Height = 61

Shoe size = -23.97 + 0.49*61 = 5.92, which will be approximately 6.

f)

It comes out to be 6 in the last part.

If it is given 7, then the residual is 6 - 7, which is -1.