SCCC 312 - Homework Assignment 3

This assignment will use the data set given below that concerns the relationship between the prevalence of a supposed fertility enhancer and the population of Oldenburg Germany in thousands of people between 1930 and 1936.

The original data can be found in: Ornithologische Monatsberichte, 44, No.2, Jahrgang, 1936, Berlin, and 48, No.1, Jahrgang, 1940, Berlin, and Statistiches Jahrbuch Deutscher Gemeinden, 27-33, Jahrgang, 1932-1938, Gustav Fischer, Jena. The actual data used below is estimated from the graph in Box, Hunter, and Hunter's Statistics For Experimenters. 

X	PEOPLE
140	55.5
148	55.5
175	64.9
195	67.5
245	69.0
250	72.0
250	75.5
Using MINITAB, perform a linear regression to predict the population (in thousands) from the prevalence of the fertility enhancer. To do this, choose Fitted Line Plot... in the Regression submenu of the Stat menu. Since we will want to look at the residuals, make sure to choose the Storage... of the Residuals. To make a Q-Q plot of the residuals, you do not need to do all the work you did on Homework 2, choose Probability Plot... under the Graph menu. You will want to unselect the Options... Include confidence intervals in plot if it is selected. Turn in these two graphs with the answers to the questions below.

  1. If an X value of 210 were used, what would the predicted population be?
  2. Assuming the errors are normal, how far off do you expect your prediction in 1 to be? (Some amount, some percent of the time)
  3. Say you were asked to repeat questions 1 and 2 for X=75. Why would you not want to trust the answers you got? (Again, assume the errors are normal. This should be a one or two sentence answer.)
  4. From the Q-Q plot, how confident are you that the errors seem normal? Why? (Give me your gut instinct here, not some elaborate statistical answer.)
  5. Using the r2 describe how much of the changes/error in the population measurements seems to be explained by knowing how much of X was present.
  6. Does it seem that an increase in X causes a change in the population?