Sum2 2011
NCSU
ST512
QUIZ 1
NAME
We are interested in studying the relationship, if any, between yield (Y, in bushels/acre), and
rainfall (X, inches/yr) on corn raised in six midwestern states from 1890 to 1927. Our main
goal is to find out an equation that will help in the prediction of corn yield for a given
rainfall.
Scatter plot
After observing the scatter plot for Yield vs Rainfall, we decided to fit a linear regression equation to
the observed data with Yield as dependent variable and Rainfall as independent (explanatory)
variable.
1. Explain briefly why the method of least squares is used to estimate the regression equation.
2. The regression parameter estimates are presented below.
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July 07, 2011
Sum2 2011
NCSU
ST512
QUIZ 1
Parameter Estimates
Parameter Standard
Estimate
Error t Value Pr > |t|
95% Confidence
Limits
Variable
DF
Intercept
1
23.55210
3.23646
7.28 <.0001 16.98825 30.11595
rainfall
1
0.77555
0.29386
2.64 0.0122
0.17957
1.37153
a. Write down the estimated linear regression equation
b. Interpret the regression coefficient (slope)
3. Summary statistics for Rainfall and yield
Simple Statistics
Variable
N
Mean
Std Dev
Sum
Minimum
Maximum
rainfall
38
10.78421
2.26543
409.80000
6.80000
16.50000
yield
38
31.91579
4.36370
1213
19.40000
38.30000
Analysis of variance table
Analysis of Variance
Source
DF
Sum of
Squares
Model
114.21474
Error
Corrected Total
Mean
Square
F Value
Pr > F
0.0122
590.33578
37
a. Fill the blanks in ANOVA Table
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July 07, 2011
Sum2 2011
NCSU
ST512
QUIZ 1
b. Is the linear regression coefficient estimated by 1 significantly different from 0? Support
your answer.
c. How much of the total variation of Yield is explained by the relationship between Yield and
Rainfall?
4.
The estimated regression line and 95% confidence interval for the conditional mean of yield for
given X and the 95% prediction interval for an individual Yield when rainfall takes a given value
is presented graphically
3
July 07, 2011
Sum2 2011
NCSU
ST512
QUIZ 1
a. Give an overall evaluation of the adequacy of the fitted line to the observed trend for
the relationship between Yield and Rainfall. Will you use this equation to predict
yield? Explain
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July 07, 2011