Using the two data sets below: 1) Draw a scatterplot for each. Test whether the correlations are significant. Use 0.01 for α Give the values for t, p, and r. x y 31 107 68 78 14 125 21 112 60 87 17 124 76 77 49 92 20 118 97 x y 3.552 878 2.701 1162 3.112 1235 2.991 888 3.357 959 2.587 787 2.917 1227 3.649 835

Using the two data sets below: 1) Draw a scatterplot for each. x y 3.552 878 2.701 1162 3.112 1235 2.991 888 3.357 959 2.587 787 2.917 1227 3.649 835 I set my Window to: x-min: 0 y-min: 750 x-max: 5 y-max: 1250 If you had a different window, your graph may look a little different.

Using the two data sets below: Test whether the correlations are significant. Use 0.01 for α Give the values for t, p, and r. 𝐻 0 :𝜌=0 𝐻 𝑎 :𝜌≠0 STAT–TEST–F 𝑡=−.713 𝑝=.503 𝑟=.279 Since 𝑝>𝛼, fail to reject the null. The correlation is NOT significant.

Using the two data sets below: 1) Draw a scatterplot for each. x y 31 107 68 78 14 125 21 112 60 87 17 124 76 77 49 92 20 118 97 I set my Window to: x-min: 10 y-min: 70 x-max: 80 y-max: 130 If you had a different window, your graph may look a little different.

Using the two data sets below: 1) Draw a scatterplot for each. Test whether the correlations are significant. Use 0.01 for α Give the values for t, p, and r. x y 31 107 68 78 14 125 21 112 60 87 17 124 76 77 49 92 20 118 97 𝐻 0 :𝜌=0 𝐻 𝑎 :𝜌≠0 STAT–TEST–F 𝑡=−10.447 𝑝=6.119𝐸−6 𝑟=.965 Since 𝑝≤𝛼, Reject the null. The correlation is significant.

Section 9-2 – Equation of Best Fit for Linear Regression The only thing in Section 9-2 that is new is to use the equation of the line of best fit to make predictions about y-values. You can only use the equation to make predictions if the correlation is significant!! That's why we ran the tests in 9-1 to determine whether the correlation is significant or not. When you run STAT-TEST-F, you get the equation of the line of best fit, too. Using the data from Example 7 in 9-1, we got the following: 𝑦=𝑎+𝑏𝑥; 𝑎=104.061, and 𝑏=50.729, so the equation is 𝑦=50.729𝑥+104.061

Section 9-2 – Equation of Best Fit for Linear Regression Example 3 - (Page 516) Use the equation of best fit from Example 7 in 9-1 to predict the expected company sales for the following advertising expenses. a) 1.5 thousand b) 1.8 thousand c) 2.5 thousand Remember, we have already determined that the correlation is significant, so this equation can be used for making predictions. 1) Plug each value of x into the equation to find the y-value prediction. 𝑦=50.729 1.5 +104.061≈180.155, 𝑜𝑟 $180,155 𝑦=50.729 1.8 +104.061≈195.373, 𝑜𝑟 $195,373 𝑦=50.729 2.5 +104.061≈230.884, 𝑜𝑟 $230,884 2) Enter the equation into y = ( 𝑦=50.729𝑥+104.061) Use 2nd Window to set beginning of table, then use 2nd Graph to see the y-value for each x.

Assignments: Classwork: Pages 517-518 # 9-12 All Homework: Pages 517-520 #14-28 Evens Run the hypothesis test to prove significance, and then make predictions if possible. QUIZ on 9-1 and 9-2 next class!!