Project – STAT 3001

Part I.  Analyze Data
Open the fileCARS using menu option Datasets and then Elementary Stats, 9th Edition.  This file contains some information about different cars.How many observations are there in this file?

Analyze the data in this file and complete the following table, indicating for each variable what type of data it represents.
Variable    Qualitative/ Quantitative    Discrete/ Continuous/ Neither    Level of Measurement
Car
Length
Cylinders
Size
Braking
Would you consider this data to represent a sample or a population?

Part II. ScatterPlots
. Create a scatterplot for the data in the Weight and Braking columns.Paste it here.You may need to resize the plot once it is in this file.
. Explain the visual relationship between Weight and Braking distance of the cars.
Create a scatterplot for the data in the Weight and the City MPG columns. Paste it here.You may need to resize the plot once it is in this file.
Explain the visual relationship between Weight and City MPG.

Part III.  Correlation
Using Stat Disk, calculate the linear correlation between the data in the Weight and Braking columns.List the steps used for the calculation and give the resulting correlation coefficient.
Explain the mathematical relationship between Weight and Braking based on the linear correlation coefficient.  Be certain to include comments about the magnitude and the direction of the correlation.

List the sample size and the degrees of freedom for this computation.
Using Stat Disk, calculate the linear correlation between the data in the Weight and City MPGcolumns.
Compare and contrast these two relationships:

Weight and Braking distance
Weight and City MPG

How are they similar? How are they different?

[
“Types of Correlation”]

Part IV.  Simple Regression
Let’s say that we wanted to be able to predict the Braking distancein feet for a car based on its weight in pounds. Using this sample data, perform a simple-linear regression to determine the line-of-best fit. Use the Weight as your x (independent) variable and braking distance as your y (response) variable.Use 4 places after the decimal in your answer.

Answer the following questions related to this simple regression

What is the equation of the line-of-best fit?  Insert the values for bo and b1from above into y = bo + b1x.
What is the slope of the line?  What does it tell you about the relationship between the Weight (Pounds)and Braking distance(Feet) data? Be sure to specify the proper units.

What is the y-intercept of the line?  What does it tell you about the relationship between the Weight and Braking distance?

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 effect would you predict this would have on the braking distance of the car?  Relate this to the Braking distance you found for a car weighing 2650 pounds in the previous question.
Find the coefficient of determination (R2 value) for this data.  What does this tell you about this relationship?

Part V.  Multiple Regression
Let’s say that we wanted to be able to predict the city miles per gallon for a car using

•    Weight in pounds
•    Length in inches
•    Cylinders

Using this sample data, perform a multiple-regression using Weight, Length, Cylinder, City.   Select City (Column 8) as your dependent variable.

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 3 decimal places.]
What would you predict for the City MPG earnings of a car whose

•    Weight is 3410 pounds
•    LENGTH is 130 inches
•    Cylinders is 6
What is the R2 value for this regression?  What does it tell you about the regression?

Col 1    Col 2    Col 3    Col 4    Col 5    Col 6    Col 7    Col 8    Col 9

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