Consider the data in the following table where speed denotes the speed in miles per hour of a car before beginning to break and distance the distance in feet covered before the car comes to a stop $($note that there are $16$ observations$)$:

distance $843646683248525664665470929312085$

speed $18191919202020202022232424242425$

State the answer and provide the R code used for the following questions:

a$)$ Create a dataframe in R called cars that contains the information above. Print it in your RStudio and check its naming matches the naming above. You do not need to state an answer $($other than code$)$ for this question. $[1$ mark$]$

b$)$ Fit a simple linear regression with speed as the predictor and distance as the outcome. What are the slope and intercept coefficients? $[1$ mark$]$

c$)$ Provide a $90$ percent confidence interval for the slope coefficient of the regression. $[1$ mark$]$

d$)$ Predict the distance it would take a car driving at $30$ miles per hour to stop according to the model you have fit to the data. $[1$ mark$]$

e$)$ Perform a basic check using a graphical approach of whether the relationship between speed and distance is linear. Explain your conclusion. $[1$ mark$]$