1. Car washes and Repairs

Observations can be fairly simple and straightforward. Notice how the table gives the units for y. What do you think the units for x should be?

Mean Standard Deviation
x = number of car washes per year 6.4 3.78
y = repair costs for last year $955.30 $323.50

The correlation for these two variables is r = -0.71.

Questions you should be asking yourself during the test

  • What does the negative number imply?
  • How do you intepret a negative correlation number?
  • What is the range of any correlation?
  • Given knowledge of the range of the correlation, does r=-0.71 mean anything different to you?

1a. Find the equation of the least-squares regression lines

  • What are the units of the equation of y?
  • You have the equation, but start thinking about the sign of the slope and y-intercept. What does a negative slope imply?

1b. Interpret the slope of the least-squares line in context.

If you start thinking about what the data implies as you are writing out the equations, then you can start writing the “English” part of the exam.
Words like “in context” and “interpret” mean you should be writing sentances about your observations. Don’t forget units.

DRAW A PICTURE with meaningful units on the x and y axes. Dollars ($) on the y, and “# of times washed / year” on the x.

The picture should reflect both the correlation (r=-0.71) and the slope (-60.7).

1c. What is the r2 value? Interpret this value in context.

1d. Based on this data, can we conclude that washing your car frequently will reduce repair costs? Explain

2. Mass of Chicken Eggs

3. Linear relationship of Sodium deficiences and Sodium Intake

deficit = c(100, 200, 570, 850, 700, 425, 375, 325, 450, 850)
intake =  c(110, 180, 610, 790, 750, 390, 420, 380, 300, 790)