1) Seven families were randomly selected by a supermarket chain to participate in a study. The number of children in each family, along with their average weekly grocery bill, is given below:

# of children 2 3 2 5 3 0 7

Grocery bill ($) 140 155 150 245 175 90 265

a) Draw a scatterplot for the data.

b) Calculate the linear correlation coefficient r.

c) Describe the apparent correlation between the number of children and the size of the grocery bill. Explain in plain language what this relationship means.

d) Determine the equation of the regression line.

e) Use the regression equation to predict the average weekly grocery bill for a family with: 1 child; 5 children. Explain what these predictions mean.

f) Plot the 2 points of the regression line (done in e) ) and draw the line.

g) Interpret the slope of the regression line.

h) Compute the coefficient of determination, r 2 .

i) Interpret r 2 .

j) How good is the prediction given by the regression line in this instance?

2) Octane ratings and prices per gallon for 5 grades of gasoline were once as follows:

Octane 87 89 92 94 97

$/gal. 1.219 1.259 1.399 1.479 1.559

a) Plot the points on a scatterplot and draw the regression line on the same axes. (Note: you should round to 3 decimal places throughout this exercise.)

b) Calculate the predictions from the regression line for each octane rating in the data.

c) Calculate the residual for each data point. Which octane grade is priced most below its prediction (hence, is the best deal for the octane it provides)? Which grade is most overpriced?

3) The number of people living on American farms has declined steadily during the last century. Here are data on the farm population (millions of persons) from 1935 to 1980:

Year 1935 1940 1945 1950 1955 1960 1965 1970 1975 1980

Pop. 32.1 30.5 24.4 23.0 19.1 15.6 12.4 9.7 8.9 7.2

a) Draw a scatterplot for the data.

b) Determine the regression equation.

c) According to the regression line, how much did the farm population decline each year on average during this period?

d) What percent of the observed variation in farm population is accounted for by the relationship with the year?

e) Use the regression equation to predict the number of people living on farms in 1990. Is this an interpolation or an extrapolation? Is the result reasonable? Why or why not?