# ST3002: Correlation and Regression

## Overview

For this Performance Task, you will perform a comparison of different cars, develop a linear regression equation and a multiple regression equation, and use these things to make a decision about buying a car.

**Professional Skills: **Written Communication, Oral Communication, Technology and Quantitative Fluency are assessed in this Competency.

Your response to this Assessment should:

- Reflect the criteria provided in the Rubric.
- Adhere to the required assignment length.

This Assessment requires submission of one (1) file, a report containing calculations and analysis of statistics relating to different cars. Save this file as** ST3002_firstinitial_lastname** (for example, ST3002_J_Smith).

You may submit a draft of your assignment to the Turnitin Draft Check area to check for authenticity. When you are ready to upload your completed Assessment, use the **Assessment** tab on the top navigation menu.

## Instructions

Before submitting your Assessment, carefully review the rubric. This is the same rubric the assessor will use to evaluate your submission and it provides detailed criteria describing how to achieve or master the Competency. Many students find that understanding the requirements of the Assessment and the rubric criteria help them direct their focus and use their time most productively.

#### Choosing the Right Car for You

You are considering buying a new car and want to explore the relationship between different characteristics of certain cars. Namely, you are concerned about braking distance and gas mileage in the city. In addition, you want to make some predictions about some of the characteristics of the cars. Perform the following calculations in Statdisk and include it in a report that you can take to your car dealer.

**To prepare for this Assessment:**

Open the file **CAR Measurements** using menu option **Datasets **and then **Elementary Stats, 13 ^{th} Edition in Statdisk**. This file contains information, such as size, weight, length, braking distance, cylinders, displacement, city miles per gallon (MPG), highway MPG, and GHG (greenhouse gas emissions), for 21 cars.

Perform the following tasks to help you determine which car is right for you:

- Scatterplots, Correlations, and the Correlation Coefficient
- Weight vs. Braking Columns
- Create a scatterplot for the data in the Weight and Braking columns. Paste it in your report.
- Using Statdisk, calculate the linear correlation between the data in the Weight and Braking columns. Paste your results in your Word document.
- Explain the mathematical relationship between weight and braking based on the linear correlation coefficient. Be certain to include comments about the magnitude (strength) and the direction (positive or negative) of the correlation. As weight increases, what happens to the braking distance?

- Weight vs. City MPG
- Create a scatterplot for the data in the Weight and the City MPG columns. Paste it in your report.
- Using Statdisk, calculate the linear correlation between the data in the Weight and City MPG columns. Paste your results in your Word document.
- Explain the mathematical relationship between weight and city MPG based on the linear correlation coefficient. Be certain to include comments about the magnitude and the direction of the correlation. As weight increases, what happens to the city MPG?

- Compare the correlations for weight and braking distance with that of weight and city MPG. How are they similar? How are they different?

- Weight vs. Braking Columns
- Linear Regression and Prediction
- Let’s say that we wanted to be able to predict the braking distance in feet for a car based on its weight in pounds.
- Using this sample data, perform a linear regression to determine the line-of-best fit. Use weight as your x (independent) variable and braking distance as your y (response) variable. Use four (4) places after the decimal in your answer. Paste it in your report.
- What is the equation of the line-of-best fit (linear regression equation)? Present your answer in y = bo + b1x form.
- What would you predict the braking distance would be for a car that weighs 2650 pounds? Show your calculation.
- Let’s say you want to buy a muscle car that weighs 4250 pounds. What would you predict the braking distance would be for a muscle car that weighs 4250 pounds? Show your calculation.
- What effect would you predict weight would have on the braking distance of the car? Compare the breaking distance of the 2650-pound car to the 4250-pound car.
- Calculate the coefficient of determination (R2 value) for this data. What does this tell you about this relationship?

- Let’s say that we wanted to be able to predict the braking distance in feet for a car based on its weight in pounds.
- Multiple Regression
- Let’s say that we wanted to be able to predict the city MPG for a car using weight in pounds, length in inches, and cylinders. Using this sample data, perform a multiple-regression line-of-best-fit using weight, length, cylinder, and city MPG.
- Select City MPG (Column 8) as your dependent variable. Paste it in your report.
- What is the equation of the line-of-best fit? The form of the equation is: Y = bo + b1X1 + b2X2 + b3X3 (fill in values for bo, b1, b2, and b3). Round coefficients to three (3) decimal places.
- What would you predict for the city MPG of a car whose (1) Weight is 3410 pounds, (2) LENGTH is 130 inches, and (3) Cylinders is 6?

- What is the R2 value for this regression? What does it tell you about the regression?

- Making Decisions Based on Data
- Based on the information gathered in this task on the relationship between weight and braking distance and weight and city MPG, which of the 21 cars listed would you choose to buy, and why?