Please notice that there are TWO parts to this. Module 10 Group Homework You may

Question

Please notice that there are TWO parts to this.

Module 10 Group Homework You may either hand write your answers to the questions below on notebook paper or you may type them up in a document. Remember to convert your file to a pdf before submitting it. 1. 4] During the 2015 National Football League (NFL) season the points per game and the number of wins for each team were recorded. The data is summarized below. Using the scatter plot, describe the relationship between points per game and number of wins for the 2015 NFL season. What are the explanatory and response variables? Why might we want to fit a regression line to these data? a. b. C. NFL 2015 Season Points per Game 5] Continuing from problem 1, the summary statistics for the points per game and the number of wins for each team are summarized below. 3.8 Points per game: average 22.8, SD Wins: average = 8, SD = 3.05, r 0.77 a. Use the summary statistics above to calculate the regression line y bo +bx between points per game and number of wins using points per game as the independent variable. Interpret the slope and the intercept in this context. Be specific. Use the regression line to predict the number of wins for a team that had a statistic of 20 points per game. In the data set, a team that had a statistic of 20 points per game won 4 games. Calculate the residual for this team and explain its meaning. Would it be appropriate to use this linear model to predict number of wins for a team with a statistic of 27 points per game?Explain why or why not b. c. d. e.

Explanation / Answer

1.
a) In the scatterplot, there is linear positive relationship between points per game and number of wins.

b)
The explanatory variable is points per game and response variable is number of wins.

c)
The scatterplot shows a linear positive relationship between points per game and number of wins. So, it is better to fit a regression line to this data.

2.
a) Number of data points in scatter plots = 30
Sxx = n * (SD of Points per game)2 = 30 * 3.82 = 433.2
Syy = n * SD of Wins = 30 * 3.052 = 279.075

r = 0.77 => r2 = 0.5929

Now, r2 = S2xy/ Sxx * Syy

S2xy = r2 * Sxx * Syy =  0.5929 * 433.2 * 279.075 = 71678.82

Sxy = sqrt(71678.82) = 267.729

Slope of the regression line, b1 = Sxy / Sxx = 267.729 / 433.2 = 0.618

Intercept of the regression line, b0 = Mean(Wins) - b1 * Mean(Points per game)

= 8 - 0.618 * 22.8 = -6.09

So, the regression line is y = -6.09 + 0.618 x

b.

Interpretation of slope - With one point increase in points per game, the number of wins is increased by 0.618.

Interpretation of intercept - When points per game is 0, the number of wins is -6.09. (Although it is not practical).

c.

When points per game is 20,

y = -6.09 + 0.618 * 20 = 6.27

The predicted number of wins is 6.27

d.

Residual =  Observed value - Predicted value = 4 - 6.27 = -2.27

The prediction error of the regression when points per game is 20 is -2.27

e.

Yes, it is appropriate to use the linear model to predict number of wins for a team with a statistic of 27 points per game because the data points (points per game) used in the calculation of regression equation is between 15 to 30 and 27 lies in this range.

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