Download Linear Regression Act 8 Finding and Interpreting Standard

Linear Regression Act 8
Finding and Interpreting Standard Deviation of the Residual Errors
Standard Error is a useful measure in regression analysis. It not only tells the average distance points are
from the regression line, but it also tells us the average amount of error if we make a prediction with the
regression line in the scope of the x values.
(#1-3) For each of the following problems, write two sentences to interpret the two meanings of the
standard deviation of the residual errors. Include the appropriate units in your sentences.
1. The x variable is the number of cars sold and the y variable is the total profit in thousands of dollars.
(standard error = 62.6297)
2. The x variable is the number of pounds of fertilizer used and the y variable is the number of flowers
per square foot. (standard error = 1.041)
3. The x variable is the week and the y variable is the stock price in dollars.
(standard error = 5.8286)
(#4-5) standard deviation of the residual errors is difficult to compute by hand. Let’s try to calculate
the standard deviation of the residual errors with a relatively small data set. You do not need to write
sentences for #4 and #5. Just calculate se .
4. For the following ordered pairs, the least squares regression equation is yˆ  2.93  1.24 x
Make a scatter plot of the ordered pairs and draw the regression line on the scatterplot.
Calculate the residuals  y  yˆ  for each x value and make a residual plot. Now square the
residuals and find the SSE (sum of squared errors). Then find the standard deviation of
residual errors using the formula se 
x y
1
2
3
4
5
6
7
8
3
8
4
11
7
12
8
15
Predicted ŷ
Error (Residual)
SSE
where n is the number of ordered pairs.
n2
 Error 
2
5. For the following ordered pairs, the least squares regression equation is yˆ  13.90  2.01x
Make a scatter plot of the ordered pairs and draw the regression line on the scatterplot.
Calculate the residuals  y  yˆ  for each x value and make a residual plot. Now square the
residuals and find the SSE (sum of squared errors). Then find the standard deviation of
residual errors using the formula se 
X y
1
2
3
4
5
6
7
0
Predicted ŷ
Error (Residual)
SSE
where n is the number of ordered pairs.
n2
 Error 
2
11
10
6
7
5
1
0
15
(#6-9) As you can see, Standard Error is difficult to compute by hand, but we can find the Standard
Deviation of the Residual Errors with any statistics software (Statcrunch, Minitab or Statcato). Use
whatever software you are most familiar with.
6. Open the Bear Data. Let the chest size of the bear in inches be the explanatory variable and the
weight of the bear in pounds be the response variable. Use your Statistics software to find the standard
error. Write two sentences to interpret the two meanings of the standard error. Include the
appropriate units in your sentences.
7. Open the Bear Data. Let the age of the bear in months be the explanatory variable and the length of
the bear in inches be the response variable. Use your Statistics software to find the standard error.
Write two sentences to interpret the two meanings of the standard error. Include the appropriate units
in your sentences.
8. Now open the Health Data. Let the men’s height in inches be the explanatory variable and the men’s
weight in pounds be the response variable. Use your Statistics software to find the standard error.
Write two sentences to interpret the two meanings of the standard error. Include the appropriate units
in your sentences.
9. Now open the Health Data. There does not appear to be any relationship between height and pulse
rate. Let the women’s height in inches be the explanatory variable and the women’s pulse rate in beats
per minute be the response variable. Use your Statistics software to find the standard error. Write two
sentences to interpret the two meanings of the standard error. Include the appropriate units in your
sentences. What do you notice about the standard error when there is not any correlation?