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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: y ^ = a + bx size 12{y=a+ ital "bx"} {}
  • 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
  • y ^ = 337 , 424 . 6478 + 0 . 5463 x size 12{y= - "337","424" "." "6478"+0 "." "5463"x} {}
  • 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: y ^ = a + bx size 12{y=a+ ital "bx"} {}
  • 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: y ^ = a + bx size 12{y=a+ ital "bx"} {}
  • 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
  • y ^ = 65 . 0876 + 7 . 0948 x size 12{y="65" "." "0876"+7 "." "0948"x} {}
  • 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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