2) Lamb's-quarter is a common wheat that interferes with the
growth of corn. An agriculture researcher planted corn at the same
rate in 16 small plots of ground, then weeded the plots by hand
to allow a fixed number of lamb's-quarter plants to grow in each
meter of corn row. No other weeds were allowed to grow. Here are
the yields of corn (bushels per acre) in each of the plots
(data provided by Samuel Phillips, Purdue University):
Weeds | Corn |
0 | 166.7 |
0 | 172.2 |
0 | 165.0 |
0 | 176.9 |
1 | 166.2 |
1 | 157.3 |
1 | 166.7 |
1 | 161.1 |
3 | 158.6 |
3 | 176.4 |
3 | 153.1 |
3 | 156.0 |
9 | 162.8 |
9 | 142.4 |
9 | 162.8 |
9 | 162.4 |
The output below has been obtained from WebStat for the data
listed above. (5 Points)
Simple linear regression results:
Independent variable: var1
Dependent variable: var2
Sample size: 16
Correlation coefficient: -0.4596
(See fitted line plot in Graphics Panel.)
Estimate of sigma: 8.006156
Parameter Estimate Std. Err. DF Tstat Pval
Intercept 166.48334 2.734623 14 60.879814 0
var1 -1.1102564 0.5733327 14 -1.9364958 0.0366
- a) Indicate the exact values for slope, y-intercept, the regression equation,
and the correlation coefficient obtained from WebStat. What is the explanatory
variable and what is the response variable? Comment on the relationship.
- b) Use this regression equation to predict the corn yield for 5, 10, and
100 weeds per meter. Which of these predictions are meaningful, which not?
Explain your answer.
- c) Below is a plot of the residuals versus Weeds. Does the residual
plot show any unusual pattern or do you think that, based on this
residual plot, our least squares regression line describes the
data reasonably well?