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24. (Correlation) A researcher wants to determine if there is a linear relationship between height and weight. The following
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-----------------------------Please find R code

age=c(10,15,45,32,66,75,81,55,45)
height=c(4,5.7,5.5,5.2,6,5.2,5.1,5.9,5.8)
plot(age,height,main="Regression",col="red")
fit=lm(height~age)
fit$coefficients
abline(fit)
summary(fit)
cor(age,height)
cor.test(age,height)
qt(0.975,9-2) #Critical value

---------------------------------------------------------OUTPUT

summary(fit)

Call:
lm(formula = height ~ age)

Residuals:
Min 1Q Median 3Q Max
-1.0519 -0.4227 0.1408 0.4530 0.6042

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 4.964121 0.455303 10.903 1.21e-05 ***
age 0.008780 0.008645 1.016 0.344
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.6107 on 7 degrees of freedom
Multiple R-squared: 0.1284,   Adjusted R-squared: 0.003943
F-statistic: 1.032 on 1 and 7 DF, p-value: 0.3436

cor.test(age,height)

   Pearson's product-moment correlation

data: age and height
t = 1.0157, df = 7, p-value = 0.3436
alternative hypothesis: true correlation is not equal to 0
95 percent confidence interval:
-0.4012218 0.8259319
sample estimates:
cor
0.358399

> qt(0.975,9-2)
[1] 2.364624

-----------------------------------------------------------------------------

Scatter plot with line of best fit

height 4.0 4.5 50 5 60 이 age 10203040 506070 80 Regression

The line of best fit is :- Height = 4.964121 +  0.008780*(age)

Correlation is found to be 0.358399

P value from the output above is 0.3436,, hence we reject H0 and conclude correlation is not significant

Critical value at 7 degree of freedom with alpha 0.05 is  2.364624

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