Question 9 Data on estimated total green forage yields at various levels of nitr

Question

Question 9 Data on estimated total green forage yields at various levels of nitrogen application are given in the table. Estimate the correlation between nitrogen level and forage output by using the Pearson's product moment correlation method and by using the Spearman's rank correlation method. Test significance of both the correlation coefficients at = 0.05. Fit the linear regression equation for the input output data in the table. 120 N (kg/ha) (x)0 20 Forage (Vha) ( 17.3 2.5 26.7 29.5 3 40 60 80 100 31.1 31.3 30.2

Explanation / Answer

x=c(0,20,40,60,80,100,120)
y=c(17.3,22.5,26.7,29.5,31.1,31.3,30.2)

cor.test(x,y)

Pearson's product-moment correlation

data: x and y
t = 4.3602, df = 5, p-value = 0.007289
alternative hypothesis: true correlation is not equal to 0
95 percent confidence interval:
0.4145035 0.9837072
sample estimates:
cor
0.8898113

spearman.test(x, y)

Spearman's rank correlation rho

data: x and y
S = 6, p-value = 0.0123
alternative hypothesis: true rho is not equal to 0
sample estimates:
rho
0.8928571

Pearson's product-moment correlation and Spearman's rank correlation are 0.8898113 and 0.8928571 respectively. And both the test are significant at 0.05 level of significance and can conclude that nitrogen level and forage output are positively significant at 0.05 level of significance.

model=lm(y~x)
summary(model)

Call:
lm(formula = y ~ x)

Residuals:
1 2 3 4 5 6 7
-3.13929 -0.10714 1.92500 2.55714 1.98929 0.02143 -3.24643

Coefficients:
Estimate Std. Error t value Pr(>|t|)   
(Intercept) 20.43929 1.79266 11.40 9.08e-05 ***
x 0.10839 0.02486 4.36 0.00729 **
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Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 2.631 on 5 degrees of freedom
Multiple R-squared: 0.7918, Adjusted R-squared: 0.7501
F-statistic: 19.01 on 1 and 5 DF, p-value: 0.007289

Conclusion For a unit increase on nitrogen level increases  0.10839 at mean of forage output at 0.05 level of significance.

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