Now we fit a linear regression model using R The code and ou

Now, we fit a linear regression model using R. The code and outputs are shown below:

reflux.ratio <- c(20,30,40,50,60)

concentration <- c(.446,.601,.786,.928,.950)

fit <- lm(formula = concentration ~ reflux.ratio) summary(fit)

confint(fit)

> summary(fit)

Call:

lm(formula = concentration ~ reflux.ratio)

Residuals:

1 2 3 4 5

-0.0292 -0.0077 0.0438 0.0523 -0.0592

Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 0.208200 0.073771 2.822 0.06661 reflux.ratio 0.013350 0.001739 7.678 0.00459

Residual standard error: 0.05499 on 3 degrees of freedom Multiple R-squared: 0.9516, Adjusted R-squared: 0.9354 F-statistic: 58.95 on 1 and 3 DF, p-value: 0.004591

> confint(fit)

2.5 % 97.5 %

(Intercept) -0.026572668 0.44297267

reflux.ratio 0.007816355 0.01888364

o. Does the CI include zero? Can we conclude, based on the CI, that the assumed linear association between flux ratio and ethanol concentration is significant? Explain.

p. Now perform a formal hypothesis test about ?1; that is, H0: ?1 = 0 Ha: ?1 ? 0 (Note: you don

Solution

R-squared: 0.9354 F-statistic: 58.95 on 1 and 3 DF, p-value: 0.004591

> confint(fit)

2.5 % 97.5 %

(Intercept) -0.026572668 0.44297267

reflux.ratio 0.007816355 0.01888364

o. Does the CI include zero? Can we conclude, based on the CI, that the assumed linear association between flux ratio and ethanol concentration is significant? Explain.

95% CI = ( 0.007816355, 0.01888364) does not contain zero

We can conclude that linear association between flux ratio and ethanol concentration is significant.

p. Now perform a formal hypothesis test about ?1; that is, H0: ?1 = 0 Ha: ?1 ? 0 (Note: you don