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1. This data was collected from nine homes in an exclusive neighborhood:
Price
In dollars
Floor space
in sq. ft.
Mean
Standard Deviation
336000
9000
3000
150
We wish to predict the price of a home based on the floor space. The correlation is r = 0.85
a)
Identify the explanatory variable and the response variable.
b)
Find the least squares regression equation.
c)
Identify and interpret the slope.
d)
Find the predicted price of a 2500 sq. ft. home.
f)
Find the residual for a 3200 sq. ft. home which just sold for $350,000.
2.
A university area pizza shop uses data from previous years to see if its annual revenue in dollars can be
predicted by student enrollment at the university. The linear regression equation to predict revenue from
^
enrollment is y  56800  5.4 x .
a) Identify the explanatory variable and the response variable.
b) Sketch a graph of the regression line.
c) Predict the annual revenue the pizza shop may expect when the student enrollment is 10,000.
d) Identify and interpret the slope and the y-intercept of the above equation.
e) Part of the data set included the year 1998, for which revenue was $130,000 while student enrollment was
14,000. Find the residual.
3.
An online clothing retailer gathered data from select customers to study a relationship between annual
salary and annual purchases from the company. The summary statistics, in dollars, are:
Annual purchases
Annual salary
Mean
540
51,000
Standard deviation
200
16,000
The correlation was found to be .80
a) Build the least squares regression equation to predict annual purchases based on salary.
b) Predict the annual purchases for a customer with annual salary of $64,000.
c) One customer had a salary of $45,000, and spent $600. Find the residual for that customer.
4
Restaurant ratings by customers follow a 30-point scale with higher ratings indicating better quality.
In a certain city, the ratings had a mean of 20 with a standard deviation of 3.2. The average cost of a
meal at these restaurants was $80, with a standard deviation of $20. The correlation between the two
variables was found to be 0.64. We wish to build the least squares regression line to predict the cost of a
meal at a restaurant based on its quality rating.
a)
Identify the explanatory variable and the response variable.
b)
Find the least squares regression equation.
c)
Identify and interpret the slope.
d)
Identify and interpret the y-intercept.
e)
Find the predicted cost of a meal for a restaurant with a quality rating of 22.
f)
If you actually spent $75 for a meal at the restaurant in part (e), find the residual.
5.
For selected brands of breakfast cereals, data is collected and a least squares regression line is formed to
predict calories per serving from the number of grams of sugar per serving. The equation of the line is
^
given by y  20  10 x .
a)
Identify the explanatory variable and the response variable.
b)
Identify and interpret the slope and the y-intercept of the line in the context of the problem.
c)
Predict the number of calories per serving for a brand which has 8 grams of sugar per serving.
6
Consider the following scatterplot.
a) The correlation between X and Y is approximately
A) 0.999
C) 0.60
B) 0.800
D) 0
E) between 10 and 28
b) Which of the following is a possible equation for the regression line?
^
A) y  2.4 x  15
^
B) y  2.4  15x
^
C) y  20  15x
^
D) y  20  x