MA215 Week 7

14 May MA215 Week 7

W7 Discussion “Relationship of Height and Weight”

Business Statistics

Relationship of Height and Weight

· What is regression analysis?

· In every-day language, what is a trendline, and what is it telling us?

· What does it mean to interpolate?  What does it mean to extrapolate?

· Using the given Height and Weight data set, follow the steps in the weekly video or on pages 584-585 of the textbook for performing a regression analysis using Excel to analyze the Height and Weight Data set (assume height is the input variable x and weight is the output variable y).

· Once you have performed the analysis in Excel, state the correct simple linear regression equation and use the regression equation to predict the weight (in pounds) of a person who is 65 inches tall and the weight (in pounds) of a person who is 100 inches tall.

· Why might the regression equation you have found not be a good predication of the weight of someone who is 100 inches tall?  Are you interpolating or extrapolating when you use the trendline to predict the weight?

Download the Height and Weight Table Here.

Week 7 Assignment

Question 1
Assume you have noted the following prices for paperback books and the number of pages that each book contains.
Develop a least-squares estimated regression line.

1. Go to Excel.  Create a scatter diagram for the data.  Include the trendline (regression line). Make sure from Week 1 you know what a trendline is.  It is NOT simply connecting the dots.

2. Once the scatter diagram is created, right-click on the trendline itself in the graph.  Use the “format trendline” from the menu to show the equation of the trendline and the r squared value on the graph itself.

3. Provide the coefficient of determination and explain its meaning.

4. Provide the correlation coefficient between the price and the number of pages.

5. Run the regression analysis as demonstrated in the video lecture. Follow the directions of what to analyze to test and see if x and y are related. Use α = 0.10.

1. What is your null and alternative hypotheses?

2. What is the t value?

3. What are the degrees of freedom?

4. On what basis do you reject of fail to reject the null hypothesis?

 

Question 2

The following data represent a company’s yearly sales volume and its advertising expenditure over a period of 8 years.

1. Develop a scatter diagram of sales versus advertising and explain what it shows regarding the relationship between sales and advertising.  Make sure your axes are labeled and that you have the axes correct (notice that x and  y are above the labels).  The graph should have a title that mentions the two variables.

2. Use the method of least squares to compute an estimated regression line between sales and advertising OR just show it on the graph along with your r-squared value..

3. If the company’s advertising expenditure is $200,000, what are the predicted sales? Give the answer in dollars.  (This is found using algebra and the equation of the trendline / regression line – make sure to watch your units)

4. What does the slope of the estimated regression line indicate?

W7 Project Assignment “Project Week 7”

Business Statistics

Project Week 7

For these project assignments throughout the course you will need to reference the data in the ROI Excel spreadheet. Download it here.

 

Using the ROI data set:

For each of the two majors:

1. Draw the scatter diagram of Y = ‘Annual % ROI’ against X = ‘Cost’.  Include the trendline (regression line) and the r-squared value (coefficient of determination).

2. Obtain b0 and b1 of the regression equation defined as y ̂ = b0 + b1X (y intercept and slope).

3. Calculate the estimated ‘Annual % ROI’ when the ‘Cost’ (X) is $160,000.    (algebra using the equation of the line)

Test the hypothesis:   You will need to show work for the tests you are performing – t-tests, F tests…see the end of chapter 12 to make sure you are doing a comprehensive analysis.

o H0: β1 = 0

o Ha: β1 ≠ 0

o In a highlighted box, write a paragraph or more on any observations you make about the regression estimates, coefficient of determination, the plots, and the results of your hypothesis tests.  Please note the plural nature – paragraph or MORE, hypothesis testS – there is a focus on the comprehensive nature of this final part of the project.  One way to set this part of the project up is to first talk about each test – what is it, what does it test for?  Then show your work and discuss the outcome.  Repeat this for each test.  Summarize findings at the end.

 

Grading Criteria Assignments

Maximum Points

 

Meets or exceeds established   assignment criteria

40

 

Demonstrates an understanding   of lesson concepts

20

 

Clearly presents   well-reasoned ideas and concepts

30

 

Uses proper mechanics,   punctuation, sentence structure, and spelling

10

 

Total

100