Question

1. For the following data, calculate the correlation coefficient. (Show the code)

   Y	X
   72	45
   73	38
   75	41
   76	35
   77	31

2. B.Plot the scatterplot of the data above AND add the scatterplot here. (Show code) What type of relationship do you see?
3. Using the information from problem 1 calculate the intercept and   coefficient. Then write the regression equation to explain the relationship. (Show the code)
4. Interpret the R-squared.

Answer 1

1.

> data
Y X
1 72 45
2 73 38
3 75 41
4 76 35
5 77 31
> cor(data$Y,data$X,method = "pearson")
[1] -0.8507273

Correlation between X and Y = -0.8507

2. > plot(data$X, data$Y,type = "p",main = "Scatterplot",xlab = "x", ylab = "Y")

It represents a strong linear (but negative) relationship.

3.

> model = lm(Y~X,data=data)
> summary(model)

Call:
lm(formula = Y ~ X, data = data)

Residuals:
1 2 3 4 5
-0.3069 -1.6000 1.3828 0.4172 0.1069

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 87.0483 4.4759 19.448 0.000297 ***
X -0.3276 0.1169 -2.803 0.067660 .
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 1.259 on 3 degrees of freedom
Multiple R-squared: 0.7237,   Adjusted R-squared: 0.6316
F-statistic: 7.859 on 1 and 3 DF, p-value: 0.06766

Equation : Y = 87.05 - 0.33 X

R-squared = 0.7237

Interpretation :

X explains 72.37% variability in Y

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