Using World Bank (2004) World Development Indicators; Washington: International Bank for Reconstruction & Development/ The World Bank, located in the reference section of the Learning Centre (Stats 330.9 WOR), collect a sample of data comprising cereal yield in kg/ha and fertilizer consumption in hundreds of grams /ha of arable land for the period 2000-2002 from 25 countries around the world. These data can be found in Table 3.3 pp123-126 and Table 3.2 pp 119-122 respectively.
For the regression analysis, use cereal yield as the dependent variable (Y) and fertilizer consumption as the independent variable (X). Enter the two variables into an SPSS file and carry out the following exercise:
1. Regress cereal yield (Y) on fertilizer consumption (X).
2. Produce a plot of the 30 observations, the calculated regression line and the 95% confidence limits.
3. What is the correlation between cereal yield and fertilizer consumption?
4. State whether the modeled regression relationship is significant.
5. Examine the plotted residuals and attempt to explain two of the extreme positive and negative values (max 300 words).
6. Calculate the runs test and the Durbin-Watson statistic on the residuals and indicate whether auto-correlation is present at the 0.05 significance level.
1)
We run the regression of cereal yield on fertilizer consumption. The fitted regression line is given by:
cereal yield= 2254.069+0.253 * fertilizer consumption
Regression
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Variables Entered/Removed
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Model
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Variables Entered
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Variables Removed
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Method
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1
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fertilizer consumptiona
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.
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Enter
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a. All requested variables entered.
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b. Dependent Variable: cereal yields
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Residuals Statisticsa
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|
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Minimum
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Maximum
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Mean
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Std. Deviation
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N
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Predicted Value
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2254.07
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3054.49
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2400.90
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195.404
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25
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Residual
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-2.251E3
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4481.879
|
.000
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1822.796
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25
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Std. Predicted Value
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-.751
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3.345
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.000
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1.000
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25
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Std. Residual
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-1.209
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2.407
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.000
|
.979
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25
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a. Dependent Variable: cereal yields
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|
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3) The Correlation coefficient is 0.01
4) From the ANOVA table we see that the regression is not significant at 5% level of significance.
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ANOVAb
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Model
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Sum of Squares
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df
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Mean Square
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F
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Sig.
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|
1
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Regression
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916388.422
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1
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916388.422
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.264
|
.612a
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Residual
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7.974E7
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23
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3467045.255
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|
|
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Total
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8.066E7
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24
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a. Predictors: (Constant), fertilizer consumption
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|
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b. Dependent Variable: cereal yields
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6)
The Durbin-Watson statistic is 1.588 which is close to 2 indicating there may be no or little positive autocorrelation
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Model Summary
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Model
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R
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R Square
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Adjusted R Square
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Std. Error of the Estimate
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Durbin-Watson
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|
1
|
.107a
|
.011
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-.032
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1862.000
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1.588
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a. Predictors: (Constant), fertilizer consumption
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|
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b. Dependent Variable: cereal yields
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|
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However we next perform the run test which clearly implies that the residuals are independent at 5% level.
NPar Tests
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Runs Test
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|
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Standardized Residual
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Test Valuea
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-.15308
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Cases < Test Value
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12
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Cases >= Test Value
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13
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Total Cases
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25
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Number of Runs
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15
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Z
|
.417
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Asymp. Sig. (2-tailed)
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.676
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a. Median
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7)
For less developed countries the intercept term will be very low as compared to high developed countries.
Moreover the slope of the fertilizer consumption will also be low in less developed countries indicating slow growth rate of cereal yield.
7. What differences would you expect to find between less developed and more developed countries in terms of the relationship between cereal yield and fertilizer consumption?