ICA Chapter 7 Fall 2023 (1)

In Class Activity – Chapter 7 Math 2600 Linear Regression Introduction to Statistics For this activity, we will analyze NFL team stats for the 2021 season. Specifically, we will predict the number of touchdowns (TD) a NFL team scores based on their passing yards (Pass Yds). Keep in mind these numbers are over the entire football season. The data set below can also be accessed in Google Sheets . Team Cmp % Pass Yds TD 49ers 66.7 4437 26 Bears 61.2 3635 16 Bengals 69.2 4806 36 Bills 63.4 4450 36 Broncos 65.4 3856 20 Browns 61.5 3619 21 Buccaneers 67.3 5383 43 Cardinals 70.2 4619 27 Chargers 65.7 5014 38 Chiefs 66.4 4937 37 Colts 62.2 3588 27 Cowboys 68.6 4963 40 Dolphins 65.7 3936 21 Eagles 62.2 3585 20 Falcons 65.8 3987 20 Commanders 64.7 3746 21 Giants 59.2 3463 15 Jaguars 59.8 3674 12 Jets 59.2 3959 20 Lions 66.8 3884 23 Packers 67.8 4526 39 Panthers 58.1 3573 14 Patriots 68 4098 24 Raiders 68.3 4808 23 Rams 66.9 4893 41 Ravens 64.8 4267 21 Saints 58.1 3437 29 Seahawks 65.4 3815 30 Steelers 64 4017 23 Texans 64.8 3630 21 Titans 67.1 3745 22 Vikings 65.9 4450 34 a. State the explanatory variable and the response variable. What wording in the description tells us this is how they are supposed to be set? - Explanatory variable= Passing yards, Response variable= Touchdowns. b. Generate the linear regression using StatCrunch. State the linear regression equation here. StatCrunch Directions: How to Generate a Linear Regression Graph > Stat > Regression > Simple Linear > Select the X variable and select the Y variable > Compute! Page 1 of 3

In Class Activity – Chapter 7 Math 2600 Linear Regression Introduction to Statistics - Td hat= 0.0127(pass yds)-26.3334 c. State the value of the slope and then interpret the value of the slope within the context of this problem. - Slope= 0.0127 For each additional passing yards, the predicted touchdowns increase by 0.0127. d. State the value of the y-intercept and then interpret the value of the y intercept within the context of this problem. - - 26.3334+0.0127(4300) = e. Suppose an NFL team had 4300 passing yards in a season. What would the expected number of touchdowns for that team according to our linear regression? Show your work. - Td^= -26.33 f. The Cleveland Browns had 3619 passing yards and a total of 21 touchdowns for the 2021 season. Find the residual value for this team when number of passing yards is 3619. Did the regression over or underestimate their number of touchdowns and by how much? Show your work. - Y-y^= 21-19.63= 1.37(positive value) underestimating g. State the R-squared value. Interpret its meaning within the context of this scenario. - R-sq= 0.6476, meaning that in percentage 64.76% of variation in touchdowns is explained by the variation is passing yards. h. Generate the residual plot for this data. Does it support that the linear regression is appropriate for the data or not? Why? StatCrunch Directions: How to Generate a Linear Regression with Residual Plot Graph > Stat > Regression > Simple Linear > Select the X variable and select the Y variable. Under Graphs select Residuals vs. X-values > Compute! - The residual plot supports the linear regression because (i) no pattern is seen, (ii) residuals are scattered around ‘o’ line, (iii) similar number points lie on either side of the line Page 2 of 3