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. Print your data frame with R.
2. Use R to create the scatterplot of y vs. x.
3. *Compute the correlation of x and y. Also compute the R² value. In your opinion, is the R² value large enough to be significant?
4. Use R to compute x, SD_x+, y, SD_y+.
5. *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.
6. *Check your answer with R. How close did you get?
7. *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 about 15 or more observations.

Here are some suggestions:

x variable	y variable
force on spring	displacement of spring
drop height for tennis ball	rebound height
number of bytes taken from a Twizzler candy stick	length of Twizzler after taking bites
age of automobile	selling price
miles on automobile odometer	selling price
number of carats in diamond	selling price
number of square feet in home	selling price

Use R to these questions. For each question, show the R source code and R output. 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. If you found it online, give the URL of the website.
2. Create an R data frame containing the data. Give labels to your variables. Print your dataset.
3. *Use R to obtain the correlation with R. Type the correlation to show that you found it.
4. *Obtain the R² value with R. Type the R-squared value to show that you found it.
5. *Verify that r * r = R².
6. *Obtain the regression equation with R. Type the regression equation in your submission to show that you found it.
7. Use R to create a scatterplot of y vs. x. Add the regression line to the scatterplot using the F lines function.
8. *Form the residual plot. Add the horizontal zero line. Are the residuals unbiased? Are they homoscedastic?
9. *Form the normal plot of the residuals? Add the normal line with the R qqline function. Are the residuals approximately normal? If not, are the residuals skewed, or do they have thin or thick tails.

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?