Computer, Minitab, and other printouts

Reading Data

1. A sample of men agreed to participate in a study to determine the relationship between several variables including height, weight, waist size, and percent body fat. A scatterplot with percent body fat on the y-axis and waist size (in inches) on the horizontal axis revealed a positive linear association between these variables.Computer output for the regression analysis is given below:

(a) Write the equation of the regression line (be sure to use correct notation and define your variables):

%̂𝑏𝑜𝑑𝑦 𝑓𝑎𝑡=−42.734+1.70(𝑤𝑎𝑖𝑠𝑡)

(b) Explain/interpret the information provided by R-squared in the context of this problem. Be specific.

r2 = 67.8%67.8% of the variation in percent body fat can be explained by the variation in waist size.

(c) Calculate and interpret the correlation coefficient (r).

The correlation of .823 tells us that there is a fairly strong and positive relationship between percent body fat and waist size.

(d) One of the men who participated in the study had waist size 35 inches and 10% body fat. Calculate the residual associated with the point for this individual.

Residual = = observed – predicted

Residual = 10 – 16.766 = - 6.766

%̂𝑏𝑜𝑑𝑦 𝑓𝑎𝑡=−42.734+1.70(𝑤𝑎𝑖𝑠𝑡)

A dietitian obtains the amounts of sugar (in grams) from 1 gram in each of 16 different cereals, including Cheerios, Corn Flakes, Fruit Loops, Trix and 12 others. He enters the data into Minitab (statistical software) and gets the following output:

(a) What measures of center are displayed in the data and what are their values?

TotalVariable Count Mean SE Mean StDev Variance CoefVar Minimum Q1C1 16 0.3281 0.0480 0.1920 0.0369 58.51 0.0300 0.1300   Variable Median Q3 MaximumC1 0.4100 0.4650 0.7000

Mean = 0.3281

Median = 0.4100

A dietitian obtains the amounts of sugar (in grams) from 1 gram in each of 16 different cereals, including Cheerios, Corn Flakes, Fruit Loops, Trix and 12 others. He enters the data into Minitab (statistical software) and gets the following output:

(b) What measures of spread can be found using the data?

TotalVariable Count Mean SE Mean StDev Variance CoefVar Minimum Q1C1 16 0.3281 0.0480 0.1920 0.0369 58.51 0.0300 0.1300   Variable Median Q3 MaximumC1 0.4100 0.4650 0.7000

Standard Deviation = 0.1920

IQR = Q3 – Q1 = 0.4650 – 0.1300 = 0.3350

(c) How could we determine if there are any outliers?

TotalVariable Count Mean SE Mean StDev Variance CoefVar Minimum Q1C1 16 0.3281 0.0480 0.1920 0.0369 58.51 0.0300 0.1300   Variable Median Q3 MaximumC1 0.4100 0.4650 0.7000

Use the IQR = 0.3350.

IQR X 1.5 = 0.3350 X 1.5 = 0.5025

Q3 + 0.5025 = 0.9675 Q1 – 0.5025 = - 0.3725

Compare to Minimum and Maximum values. If either are outside of this range, there are outliers. If not, there aren’t any. Because Min = 0.0300 and Max = 0.7000, there are no outliers.

t - statistic p - valueStandard errorY-intercept

SlopeCorrelation