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 20002002 from 25 countries around the world. These data can be found in Table 3.3 pp123126 and Table 3.2 pp 119122 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 DurbinWatson statistic on the residuals and indicate whether autocorrelation 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
Variables Entered/Removed

Model

Variables Entered

Variables Removed

Method

1

fertilizer consumption^{a}

.

Enter

a. All requested variables entered.


b. Dependent Variable: cereal yields

Residuals Statistics^{a}


Minimum

Maximum

Mean

Std. Deviation

N

Predicted Value

2254.07

3054.49

2400.90

195.404

25

Residual

2.251E3

4481.879

.000

1822.796

25

Std. Predicted Value

.751

3.345

.000

1.000

25

Std. Residual

1.209

2.407

.000

.979

25

a. Dependent Variable: cereal yields




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.
ANOVA^{b}

Model

Sum of Squares

df

Mean Square

F

Sig.

1

Regression

916388.422

1

916388.422

.264

.612^{a}

Residual

7.974E7

23

3467045.255



Total

8.066E7

24




a. Predictors: (Constant), fertilizer consumption



b. Dependent Variable: cereal yields




6)
The DurbinWatson statistic is 1.588 which is close to 2 indicating there may be no or little positive autocorrelation
Model Summary

Model

R

R Square

Adjusted R Square

Std. Error of the Estimate

DurbinWatson

1

.107^{a}

.011

.032

1862.000

1.588

a. Predictors: (Constant), fertilizer consumption


b. Dependent Variable: cereal yields



However we next perform the run test which clearly implies that the residuals are independent at 5% level.
NPar Tests
Runs Test


Standardized Residual

Test Value^{a}

.15308

Cases < Test Value

12

Cases >= Test Value

13

Total Cases

25

Number of Runs

15

Z

.417

Asymp. Sig. (2tailed)

.676

a. Median


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?