Question

2. Let the following data be given where X is the independent variable and Y is the dependent variable Find the correlation coefficient r a. a and B,onpfrom the sample for the model: b. Estimate +tx and the actual data Y where ε is the random error between the fitted model f by Y write the linear equation P=" dr-h Predict the value of P when x = 8 c. d.

Answer 1

a. The correlation coefficient between is 0.6744533.

cor(x,y)
[1] 0.6744533

b. The regression coefficients are Bo = 0.7143 and B1 = 1.5714.

summary(fit)

Call:
lm(formula = y ~ x)

Residuals:
1 2 3 4 5
-2.2857 0.1429 1.2857 -0.2857 1.1429

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 0.7143 1.4046 0.509 0.646
x 1.5714 0.9932 1.582 0.212

Residual standard error: 1.662 on 3 degrees of freedom
Multiple R-squared: 0.4549,   Adjusted R-squared: 0.2732
F-statistic: 2.503 on 1 and 3 DF, p-value: 0.2117

c. The regression line equation is Y^= B0^ + B1^ * X. = 0.7143 + 1.5714*X.

d.The value of Y when X=8 is 13.28571.

predict(fit,data.frame(x=8),interval = "confidence")
fit lwr upper
1 13.28571 -8.336957 34.90839