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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).
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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.
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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. OpenStax CNX. Jul 03, 2012 Download for free at http://cnx.org/content/col10522/1.40
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