According to flyer by a Prudential Insurance Company representative, the costs of approximate probate fees and taxes for selected net taxable estates are as follows:
Net Taxable Estate ($)
Approximate Probate Fees and Taxes ($)
600,000
30,000
750,000
92,500
1,000,000
203,000
1,500,000
438,000
2,000,000
688,000
2,500,000
1,037,000
3,000,000
1,350,000
Decide which variable should be the independent variable and which should be 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?
Find the estimated total cost for a net taxable estate of $1,000,000. Find the cost for $2,500,000.
Use the two points in (f) 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?
Based on the above, what would be the probate fees and taxes for an estate that does not have any assets?
What is the slope of the least squares (best-fit) line? Interpret the slope.
Yes
0.9964; Yes
$208,875.35; $1,028,325.35
Yes
No
slope = 0.5463. As the net taxable estate increases by one dollar, the approximate probate fees and taxes tend to increase by 0.5463 dollars (about 55 cents).
The following are advertised sale prices of color televisions at Anderson’s.
Size (inches)
Sale Price ($)
9
147
20
197
27
297
31
447
35
1177
40
2177
60
2497
Decide which variable should be the independent variable and which should be 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?
Find the estimated sale price for a 32 inch television. Find the cost for a 50 inch television.
Use the two points in (f) 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?
What is the slope of the least squares (best-fit) line? Interpret the slope.
Below are the average heights for American boys. (Source:
Physician’s Handbook, 1990 )
Age (years)
Height (cm)
birth
50.8
2
83.8
3
91.4
5
106.6
7
119.3
10
137.1
14
157.5
Decide which variable should be the independent variable and which should be 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?
Find the estimated average height for a one year–old. Find the estimated average height for an eleven year–old.
Use the two points in (f) 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?
Use the least squares line to estimate the average height for a sixty–two year–old man. Do you think that your answer is reasonable? Why or why not?
What is the slope of the least squares (best-fit) line? Interpret the slope.
Yes
0.9761; yes
72.2 cm; 143.13 cm
Yes
No
505.0 cm; No
slope = 7.0948. As the age of an American boy increases by one year, the average height tends to increase by 7.0948 cm.
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Source:
OpenStax, Collaborative statistics (custom online version modified by t. short). OpenStax CNX. Jul 15, 2013 Download for free at http://cnx.org/content/col11476/1.5
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