Journal Heidi asked 4 people their height and shoe size. Below are the results. 63 inches 7.5 69 inches 9 75 inches 11 50 inches 8 She concluded that there was a very strong negative correlation, stating that “For all people in the world, the taller you are the bigger your shoe size”. There are several errors in Heidi’s data, correlation test, and conclusion. Using OEA, comment on where she made errors, and how you know it (show any work, numbers, or formulas needed to support your claim).

Linear Regression

Problem A statistician wants to know if there is a correlation between PSAT math scores and the Math Studies IB exam scores. She collected the following data from 10 randomly selected students. Test Student Selected 1 2 3 4 5 6 7 8 9 10 PSAT 52 65 74 72 53 61 66 75 58 IB

Correlation? Is there a correlation, and if so, what kind is it?

Scatter plot Create a scatter plot

Now for the Line of Best Fit… 1. Plot ( 𝑥 , 𝑦 ).

2. Find the equation of the line By Hand 𝑦 − 𝑦 = 𝑠 𝑥𝑦 𝑠 𝑥 2 (𝑥 − 𝑥) Where: 𝑠 𝑥 2 = 𝑥 2 𝑛 − 𝑥 2 𝑠 𝑥𝑦 = 𝑥𝑦 𝑛 − 𝑥 𝑦

a is slope and b is the y-intercept. Y = .10910x – 1.5515 Get a line a is slope and b is the y-intercept. Y = .10910x – 1.5515

Find another point on the line 3. Plug in any value for x to get a y. Don’t go too close to the mean. Calculator: Y= Plug in formula 2nd Window (Tblset) Put Indpnt to “ask” 2nd Graph (Table) Plug in values for x and get y.

Draw the line 4. Plug in 40 and get 2.815 ≈(40, 2.8) Graph this point Connect the mean and the point.

2. Find the equation of the line Stat- Calc- LinReg- Enter y= ax + b a = .10910 b= -1.5515

Practice Draw a Scatter Plot Find the r-value and interpret it. X 2 1 3 4 5 6 Y 7 Draw a Scatter Plot Find the r-value and interpret it. Write the regression equation in terms of the y = ax + b Find ( 𝑥 , 𝑦 ) Draw the regression line. Predict y given x = 5.5 Predict x given y = 7