Walden STAT3001 Week 3 Project Latest 2020 January

STAT3001 Statistical Methods and Applications

Week 3 Project

Part I.  Analyze Data

Instructions         Answers

1.            Open the file Car Measurements using menu option Datasets and then Elementary Stats, 12th Edition.  This file contains information about measurements of various cars.  How many observations are there in this file?

2-7 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

               Size       

               Length (LN)        

               Displacement (Displa in liters)      

               Breaking Distance (Braking)         

8. Would you consider this data to represent a sample or a population? Why?         

Part II. ScatterPlots

9. Create a scatterplot for the data in the city MPG (city) and GHG (greenhouse gasses) columns where city MPG is the x value.  Paste it here.  You may need to resize the plot once it is in this file.

10. Explain the visual relationship between city MPG and greenhouse emissions. Is the relationship positive or negative, weak, moderate or strong? 

11. Create a scatterplot for the data in the length and braking distance columns. Paste it here. You may need to resize the plot once it is in this file.   

12. Explain the visual relationship between the length of the car and its braking distance.   

Part III.  Correlation

13.         Using Stat Disk, calculate the linear correlation between the data in the City MPG and GHG columns. List the steps used for the calculation and give the resulting correlation coefficient.            •               Open Stat Disk

14.         Explain the mathematical relationship between City MPG and GHG based on the linear correlation coefficient.  Be certain to include comments about the magnitude (weak, moderate, strong) and the direction (positive or negative) of the correlation.

15.         List the sample size and the degrees of freedom for this computation.       

16.         Using Stat Disk, calculate the linear correlation coefficient between the data in the length and braking distance columns.            

17.         Compare and contrast these two relationships:

City MPG and GHG

Length and braking distance

How are they similar? How are they different?

[Hint: Read Page 290 “Types of Correlation”]       

Part IV.  Simple Regression

Let’s say that we wanted to be able to predict the Highway MPG of a car based on its length. Using this sample data, perform a simple-linear regression to determine the line-of-best fit. Use the Length as your x (independent) variable and Highway MPG as your y (response) variable. Use 2 places after the decimal in your answer. Refer to page 13 in the Stat Disk User’s Manual.

18.         Paste your results here:

Answer the following questions related to this simple regression

19.         What is the equation of the line-of-best fit?  Insert the values for bo and b1 from above into y = bo + b1x.

20.         What is the slope of the line?  What does it tell you about the relationship between the Length and Highway MPG data? Be sure to specify the proper units.

21.         What is the y-intercept of the line?  What does it tell you about the relationship between Length and Highway MPG?

22.         What would you predict the Highway MPG for a car that is 142 inches long? Show your calculation and round to the nearest whole number.         

23.         Let’s say you want a car that has a highway MPG of 39. Use the regression equation to predict the length of the car?  Round to the nearest whole number.           

24.         Find the coefficient of determination (R2 value) for this data.  What does this tell you about this relationship? [Hint:  see definition on Page 311.]         

Part V.  Multiple Regression

Let’s say that we wanted to be able to predict the GHG emissions based on

•             Weight

•             Length

•             Cylinders

Using this sample data, perform a multiple-regression using weight, length, cylinders, and GHG with Column 10, GHG, as your dependent variable. Refer to page 14 in the Stat Disk User’s Manual. Round to 4 places after the decimal.

25.         Paste your results here:

26.         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 4 decimal places.]

27.         What would you predict for the GHG in tons per year of a car whose?

•             Weight is 3450 lb.

•             Length is 193 inches

•             Cylinders is 6

Round to two decimal places.

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