Stats assignment. Due Saturday 3PM

Point values are given in parentheses on the right. Show all work in a neat, logical manner.

1. A shoe manufacturer is looking for a simple, reasonably accurate method for estimating a person’s shoe size. He believes that there should be a relationship between the shoe size of a person and his or her height. Data were collected from a large number of college students on their heights (in inches) and their shoe sizes (in the usual numerical shoe size units that measure length, not width; for example, 7.5 or 10). The data were then analyzed in Minitab. Consider the Minitab output below in answering the questions that follow the output.

Regression Analysis: ShoeSize versus Height

Analysis of Variance

Source DF Adj SS Adj MS F-Value P-Value

Regression 1 647.6 647.627 278.61 0.000

Height 1 647.6 647.627 278.61 0.000

Error 260 604.4 ___B___

Lack-of-Fit 33 229.8 6.964 4.22 0.000

Pure Error 227 374.5 1.650

Total 261 __A__

Model Summary

S R-sq R-sq(adj) R-sq(pred)

1.525 __C__% 51.54% 48.53%

Coefficients

Term Coef SE Coef T-Value P-Value VIF

Constant -11.82 1.31 -9.01 0.000

Height 0.3166 0.0190 16.69 0.000 1.00

Regression Equation

ShoeSize = -11.82 + 0.3166 Height

Fits and Diagnostics for Unusual Observations

Obs ShoeSize Fit Resid Std Resid

22 12.000 8.763 3.237 2.13 R

23 13.500 ___D__ -4.128 -2.84 R X

70 12.000 8.129 3.871 2.55 R

146 6.000 9.079 -3.079 -2.02 R

166 16.000 11.929 4.071 2.68 R

238 5.500 4.646 0.854 0.57 X

R Large residual

X Unusual X

a. Fill in the missing blanks in the output. Show your work below the blanks. (8)

A = _________ B = _________ C = _________ D = _________

b. For each value listed below from the output, write the symbols for the statistic and for the parameter estimated by the value. (4)

B –11.82

statistic ______ ______

parameter ______ ______

c. How many college students were included in the sample? ____________ (2)

d. The value “S = 1.525” is a measure of the variation of (2)

A. ShoeSize values around their mean.

B. Height values around their mean.

C. ShoeSize values around the regression line.

D. Height values around the regression line.

e. One student in the sample is 5 feet tall and wears a size 6.5 shoe. Compute the fitted value and residual for this observation. (4) Fitted value = _______________ Residual = _______________

f. What did the shoe manufacturer see in the original scatterplot of ShoeSize versus Height that led to the form of the regression model used in the analysis? (3)

g. Fill in the blanks: __________ of the variation in the variable _____________ is explained by the variable ____________. (4)

h. Compute the correlation between ShoeSize and Height. (3)

i. Compute the standard deviation of ShoeSize in this sample of data. (3)

j. Compare the standard deviation of ShoeSize computed in part (i) to an appropriate value from the regression analysis to explain the value of the regression model in predicting ShoeSize. (3)

k. Interpret the value of the slope coefficient in the regression model in the language of the problem. Be precise with your wording. (3)

l. Construct a 95% confidence interval for the slope of the population regression line. (4)

m. What conclusion about the relationship between ShoeSize and Height can be reached based on the confidence interval in part (l)? Explain why. (3)

n. The shoe manufacturer wanted a “reasonably accurate” model for predicting shoe size for fitting his customers. Is the regression model using a person’s height reasonably accurate for fitting shoes? Answer Yes or No, then explain your answer using appropriate value(s) from the output to support your answer. (3)