Section 3.3 Activity
Finding and Interpreting Standard Error
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 error. 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 Error is difficult to compute by hand. Let’s try to calculate standard error 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 error of the
regression using the formula se 
x y
1
2
3
4
5
6
7
8
Predicted ŷ
Error (Residual)
SSE
where n is the number of ordered pairs.
n2
 Error 
2
3
8
4
11
7
12
8
15
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 error of the
regression using the formula se 
SSE
where n is the number of ordered pairs.
n2
X y
1
2
3
4
5
6
7
0
Predicted ŷ
Error (Residual)
 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
Error with either Minitab or Statcato.
6. Open the Bear Data. If we 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, find the standard error with either Minitab or
Statcato. Write two sentences to interpret the two meanings of the standard error. Include the
appropriate units in your sentences.
7. Open the Bear Data. If we let the age of the bear in months be the explanatory variable and the
length of the bear in inches be the response variable, find the standard error with either Minitab or
Statcato. 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. If we let the men’s height in inches be the explanatory variable and the
men’s weight in pounds be the response variable, find the standard error with either Minitab or
Statcato. 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. If we 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, find the standard error with either Minitab or Statcato.
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?