Question

Use the R assignment and RStudio to answer the following questions. project 2 script.Ra Note: what is below applies to p-values only! NOTE: P-values like 2e-7 is 0.0000b02 If the p-value has a number beyond e-4, just write it as 0 l.e 3.2e-3-0.0032 1.04e-5 0 <2e-26 = 0 D Question 1 23 pts Question 1 The data set "cars" in R has data on distance (dist) and speed of various

Answer 1

Please see the R code below

data("cars")
cars
##

fit <- lm(dist~speed, data=cars)
summary(fit)

## p[rediction

newdat <- data.frame(speed= c(6,21))

predict(fit,newdat)

# confidence interval for beta1

confint(fit,"speed",level=0.95)

The results are

summary(fit)

Call:

lm(formula = dist ~ speed, data = cars)

Residuals:

Min 1Q Median 3Q Max

-29.069 -9.525 -2.272 9.215 43.201

Coefficients:

Estimate Std. Error t value Pr(>|t|)   

(Intercept) -17.5791 6.7584 -2.601 0.0123 *  

speed 3.9324 0.4155 9.464 1.49e-12 *** as the p value is less than 0.05 , hence we reject the null hypothesis

---

Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 15.38 on 48 degrees of freedom

Multiple R-squared: 0.6511, Adjusted R-squared: 0.6438

F-statistic: 89.57 on 1 and 48 DF, p-value: 1.49e-12

> predict(fit,newdat)

1 2

6.015358 65.001489

> confint(fit,"speed",level=0.95)

2.5 % 97.5 %

speed 3.096964 4.767853