Project 3

IT 223 -- Project 3

Analyzing a Bivariate Dataset

Problems marked with an asterisk (*) require a typed answer.

Part A

An electronics dealer believes that there is a positive linear relationship between the number of hours of quadraphonic programming on a cities FM station (x-variable) and sales of quadraphonic systems (y-variable). Here are the data:

Month x y

1 33.6 9

2 36.3 10

3 38.7 13

4 36.6 11

5 39.0 14

6 38.4 18
1. Enter the data into an R data frame. Give labels to x and y. Print your dataset with R.
2. Use R to create the scatterplot of y vs. x.
3. *Compute the correlation r "by hand" using R. Use the correction factor n / (n - 1) to obtain the final correlation. The correction factor is because you are using SD+ for x and y instead of SD. Print the variables that you compute.
4. *Check your answer with cor(x, y). How close are the two computations of the correlation?
5. Use R to computex, SD_x+, y, SD_y+.
6. *Compute the regression line by hand using this formula:
  y - y = (r * SD_y / SD_x) * (x - x).
  Show your work. Perform your calculations to at least 5 significant digits.
7. *Check your answer with R. How close did you get?
8. *Use your regression equation to predict how many quadraphonic systems will be sold in a month when there are 35.0 hours of quadraphonic programming played on the city's FM station. Show your work.

Part B

Collect a bivariate dataset, or find one online, containing at least 15 observations.

Here are some suggestions:

x variable	y variable
puppy's age	weight
force on spring	displacement of spring
number pages in book	weight of book
age of automobile	selling price
number of carats in diamond	selling price
number of square feet in home	selling price
square root of drop height	time to fall to ground

Use R to these questions. Add comments to your output to answer the questions that require answers.
1. *Describe your dataset and the circumstances under which you collected the data.
2. Create an R dataset containing the data. Give labels to your variables. Print your dataset using Analyze >> Reports >> Case Summaries.
3. Use R to create a scatterplot of y vs. x.
4. *Use R to obtain the correlation with R. Type the correlation to show that you found it.
5. *Obtain the R² value with R. Type the R-squared value to show that you found it.
6. *Verify that r * r = R².
7. *Obtain the regression equation with R. Type the regression equation in your submission to show that you found it.
8. *Form the residual plot. Are the residuals unbiased? Are they homoscedastic?
9. *Form the normal plot of the residuals? Are the residuals normal?

Part C

R is not needed for this part.
The heights (x) and weights (y) of a population of adult giraffes is bivariate normal with
x = 16.5 ft. SD_x = 3.8 ft. y = 2,400 lbs. SD_y = 300 lbs. r = 0.75
1. Determine the regression equation for predicting weight from height.
2. What percentage of giraffes weigh more than 2,900 pounds?
3. What is the predicted weight for a giraffe that is 20 feet tall?
4. What is the root mean squared error for predicting weight, given the height?
5. Of the giraffes that are about 20 feet tall, what percentage weigh more than 2,900 lbs?