# Walden University Positive Correlation Statistics Discussion and Presentation

Please answer the following questions: Add your answer for these 2 questions ina Microsoft word, please. No specific format needed.

One correlation you believe has a positive correlation and fully explain your

reasoning.

One correlation you believe has a negative correlation and fully explain your

reasoning

Overview (power point presentation)

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:

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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.

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.

Rubric

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, 13th 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:

1. Scatterplots, Correlations, and the Correlation Coefficient

o 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?

o 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?

o Compare the correlations for weight and braking distance with that of

weight and city MPG. How are they similar? How are they different?

2. Linear Regression and Prediction

o 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 2650pound car to the 4250-pound car.

▪ Calculate the coefficient of determination (R2 value) for this data.

What does this tell you about this relationship?

3. Multiple Regression

o 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.

o 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?

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

regression?

4. Making Decisions Based on Data

o 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?