Question

Can someone show me an example on how to fit a model using least square method in R, and make a plot to compare the observed and predicted value?

2. [20] Consider the car stopping distance example we studied in Section 2.2, with the model where d is the stopping distance, v is the velocity of the car before braking, tr is the response time, and k is a coefficient related to the ratio of the braking force and the mass fo the car. (a) [5] Fit the model (i..e, determine the parameters tr and k) to the data in the first column and the last column of Table 2.4 (on Page 75 in the le containing the data has been posted on CourseSpaces), using the least aquare method. (You will need to use software such as MATLAB or R). Make a plot to compare text, for your convenience, a CSV h your predicted stopping distance with the observed distance.

Answer 1

(a)

Since we do not have data in question, I will explain the steps with R commands. You need to replace the bold characters with your filename or directory or field names. All commands are shown in italics.

First you need to read csv file into R Studio with the below command.

Run the command to set the directory where your file resides as working directory.

setwd("Path name of directory where your csv file resides")

Read the file

file1 = read.csv("filename.csv")

Fit the model. Replace the d and v in the command below with the field names from your file (1st and last column of Table 2.4).

model = lm(d ~ v + v² - 1, data = file1)

Run the command model$coefficients to get the coefficients of the model. In the output, the coefficient of v is t and the coefficient of v² is k.

Run the below command to compare the observed and predicted value. Replace the d in the command below with the field names from your file

plot(file1$d, model$fitted.values, pch = 16, xlab = "Observed distance", ylab = "Predicted distance")

The plot should be a straight line as shown in the below image.