U.S. state fertilizer indices and growth of factor productivity levels

I use USDA data from 1960 and 2004 to create a brief exploratory analysis about what makes some states more agriculturally productive than others.

Is a higher fertilizer index associated with higher factor productivity levels?

H0: There is no correlation between fertilizer indices and the growth of factor productivity.

Ha: There is a correlation between fertilizer indices and the growth of factor productivity.

 

Both growth of factor productivity levels and fertilizer consumption indices are relative to Alabama in 1998.  Alaska and Hawaii are the only states excluded.

I run the regression analysis for the 1960 and 2004 data.  A small p-value for the 1960 data has us reject the null hypothesis and conclude the alternative hypothesis that a correlation between the two variables exists.  A larger p-value for the 2004 data has us fail to reject the null hypothesis. 

We should note that the fertilizer index variable explains such a small percentage of the variability in the response variable.  The data points are scattered far from the regression line.  We see this by the value of the R-sq value.  Over time, the fertilizer index predictor variable explains even less of the variability in the response variable. 

Regression Analysis: Factor Productivity (1960) versus Fertilizer Indices in 1960

 Analysis of Variance

Source                        DF   Adj SS    Adj MS  F-Value  P-Value

Regression                     1  0.07532  0.075324     7.75    0.008

  Fertilizer Indices in 1960   1  0.07532  0.075324     7.75    0.008

Error                         46  0.44736  0.009725

Total                         47  0.52269

 

Model Summary 

        S    R-sq  R-sq(adj)  R-sq(pred)

0.0986168  14.41%     12.55%       1.83%

  Coefficients

 

Term                          Coef  SE Coef  T-Value  P-Value   VIF

Constant                    0.4969   0.0222    22.40    0.000

Fertilizer Indices in 1960  0.0499   0.0179     2.78    0.008  1.00

  

Regression Equation

 Factor Productivity (1960) = 0.4969 + 0.0499(Fertilizer Indices in 1960)

 

 Fits and Diagnostics for Unusual Observations

            Factor

     Productivity

Obs        (1960)     Fit    Resid  Std Resid

  2        0.7057  0.5104   0.1953       2.02  R         [Arizona]

  4        0.8643  0.6561   0.2082       2.34  R  X      [California]

  8        0.8649  0.5997   0.2652       2.78  R          [Florida]

 33        0.4673  0.6438  -0.1765      -1.94     X        [Ohio]

 

R  Large residual

X  Unusual X

 

 

Regression Analysis: Factor Productivity (2004) versus Fertilizer Indices in 2004

 Analysis of Variance

Source                        DF  Adj SS   Adj MS  F-Value  P-Value

Regression                     1  0.1356  0.13556     2.12    0.152

  Fertilizer Indices in 2004   1  0.1356  0.13556     2.12    0.152

Error                         46  2.9435  0.06399

Total                         47  3.0791

 

Model Summary

       S   R-sq  R-sq(adj)  R-sq(pred)

0.252961  4.40%      2.32%       0.00%

 

Coefficients

Term                          Coef  SE Coef  T-Value  P-Value   VIF

Constant                    1.1049   0.0493    22.39    0.000

Fertilizer Indices in 2004  0.0184   0.0127     1.46    0.152  1.00

 Regression Equation

 Factor Productivity (2004) = 1.1049 + 0.0184(Fertilizer Indices in 2004)

 Fits and Diagnostics for Unusual Observations

     Factor

     Productivity

Obs        (2004)     Fit    Resid  Std Resid

  1        1.7979  1.1305   0.6674       2.67  R     [Alabama]

  2        1.6304  1.1162   0.5142       2.07  R     [Arizona]

  4        1.5297  1.2817   0.2480       1.06     X  [California]

 13        1.3554  1.3211   0.0343       0.15     X  [Iowa]

 47        0.5777  1.1679  -0.5902      -2.36  R     [Wisconsin]

 48        0.5712  1.1103  -0.5391      -2.17  R     [Wyoming]

 

R  Large residual

X  Unusual X

 09-06-16-fitted-line-plot-1

09.06.16 fitted line plot #2.png

 

We could create a prediction interval for the 1960 data, but the low R-sq value indicates that this interval will be wider than desired.

We may want to include other variables in the linear regression to see if we can better capture the changes of variability of the response variable.

 Data for this brief exploratory analysis was gathered from the USDA website, specifically this page: http://www.ers.usda.gov/data-products/agricultural-productivity-in-the-us.aspx#28268.

 

 

 

 

 

Advertisements

Leave a comment - Deja un comentario - Deixa o seu comentário

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s