The maximum discount value of the Entertainment® card for the “Fine Dining” section, Edition 10, for various pages is given below.
Page number
Maximum value ($)
4
16
14
19
25
15
32
17
43
19
57
15
72
16
85
15
90
17
Decide which variable should be the independent variable and which should be the dependent variable.
Draw a scatter plot of the ordered pairs.
Calculate the least squares line. Put the equation in the form of:
Find the correlation coefficient. Is it significant?
Find the estimated maximum values for the restaurants on page 10 and on page 70.
Use the two points in (e) to plot the least squares line on your graph from (b).
Does it appear that the restaurants giving the maximum value are placed in the beginning of the “Fine Dining” section? How did you arrive at your answer?
Suppose that there were 200 pages of restaurants. What do you estimate to be the maximum value for a restaurant listed on page 200?
Is the least squares line valid for page 200? Why or why not?
What is the slope of the least squares (best-fit) line? Interpret the slope.
The next two questions refer to the following data: The cost of a leading liquid laundry detergent in different sizes is given below.
Size (ounces)
Cost ($)
Cost per ounce
16
3.99
32
4.99
64
5.99
200
10.99
Using “size” as the independent variable and “cost” as the dependent variable, make a scatter plot.
Does it appear from inspection that there is a relationship between the variables? Why or why not?
Calculate the least squares line. Put the equation in the form of:
Find the correlation coefficient. Is it significant?
If the laundry detergent were sold in a 40 ounce size, find the estimated cost.
If the laundry detergent were sold in a 90 ounce size, find the estimated cost.
Use the two points in (e) and (f) to plot the least squares line on your graph from (a).
Does it appear that a line is the best way to fit the data? Why or why not?
Are there any outliers in the above data?
Is the least squares line valid for predicting what a 300 ounce size of the laundry detergent would cost? Why or why not?
What is the slope of the least squares (best-fit) line? Interpret the slope.
Yes
0.9986; Yes
$5.08
$6.93
No
Not valid
slope = 0.0371. As the number of ounces increases by one, the cost of the liquid detergent increases by $0.0371 (or about 4 cents).
Complete the above table for the cost per ounce of the different sizes.
Using “Size” as the independent variable and “Cost per ounce” as the dependent variable, make a scatter plot of the data.
Does it appear from inspection that there is a relationship between the variables? Why or why not?
Calculate the least squares line. Put the equation in the form of:
Find the correlation coefficient. Is it significant?
If the laundry detergent were sold in a 40 ounce size, find the estimated cost per ounce.
If the laundry detergent were sold in a 90 ounce size, find the estimated cost per ounce.
Use the two points in (f) and (g) to plot the least squares line on your graph from (b).
Does it appear that a line is the best way to fit the data? Why or why not?
Are there any outliers in the above data?
Is the least squares line valid for predicting what a 300 ounce size of the laundry detergent would cost per ounce? Why or why not?
What is the slope of the least squares (best-fit) line? Interpret the slope.
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Source:
OpenStax, Collaborative statistics homework book: custom version modified by r. bloom. OpenStax CNX. Dec 23, 2009 Download for free at http://legacy.cnx.org/content/col10619/1.2
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