Question

6. The table below describes a sample of 15 players in Major League Baseball, chosen from the starting lineups of teams in 2019. The table shows the team, age, position, height, and salary for each player, as well as several statistics from that season. These include the number of games they played (G), their batting average (AVE) (the proportion of their at-bats for which they got a hit), and their home runs (HR). Name Team Age Height G AVE HR Salary Cedric Mullins Orioles 25 173 cm 22 .094 0 $557,500 Tim Anderson White Sox 26 185 cm 123 .335 18 $1,400,000 Christin Stewart Tigers 25 183 cm 104 .233 10 $556,400 Alex Gordon Royals 35 185 cm 150 .266 13 $20,000,000 Jonathan Schoop Twins 27 185 cm 121 .256 23 $7,500,000 Marcus Semien Athletics 29 183 cm 162 .285 33 $5,900,000 Yandy Diaz Rays 28 188 cm 79 .267 14 $558,400 Randal Grichuk Blue Jays 28 188 cm 151 .232 31 $5,000,000 Josh Donaldson Braves 33 185 cm 155 .259 37 $23,000,000 Joey Votto Reds 36 188 cm 142 .261 15 $25,000,000 Cody Bellinger Dodgers 24 193 cm 156 .305 47 $605,000 Ryan Braun Brewers 35 188 cm 144 .285 22 $19,000,000 Maikel Franco Phillies 27 185 cm 123 .234 17 $5,200,000 Ian Kinsler Padres 37 183 cm 87 .217 9 $3,750,000 Marcell Ozuna Cardinals 28 185 cm 130 .241 29 $12,250,000 Suppose that we want to try to predict a player's height based on their age. (a) Before doing any calculations, does it seem likely that there will be a strong association between these two variables? If so, which direction do you expect for the association? Yes, it seems likely that there is a strong positive association Yes, it seems likely that there is a strong negative association No, it does not seem likely that there is a strong association (b) Calculate the value of the correlation coefficient, r , using a calculator. r = (c) Interpret the value of r : the correlation is Select an answer and Select an answer . (d) Find the equation of the regression line for this association (note: this may not be meaningful, depending on the value of r , but we can still use it for practice). ˆ y = x + (e) Ignoring the possibility that the regression line may not be a good fit for the data, use this regression line to predict the height of a player who is 26 years old. cm

Answer 1

(a) In this question, we can focus on the columns for Age and Height only.

Looking into it, we can see that, we have some players with similar ages of 24, 25, 26 that have totally different heights, 193, 173, 183 and 185.

We also can see that some players with same height of 185 have very different ages, like 26, 35, 27, 28.

This means that it doesn't appear to be a relationship between age and height in this case.

So, the the best answer is the last on: "No, it does not seems likely that there is a strong association."

(b) Using a calculation tool, we can calculate the correlation between the columns "Age" and "Height". The others are not used.

The correlation coefficient obtained when we do that is approximately 0.1207.

(c) Since the correlation coefficient is positive, the first dropdown is "positive".

Since the correlation coefficient is close to 0 (not close to 1 or -1), the answer weak or negligible. Since it is very close to zero, it probably is negligible, but this classification is relative.

(d) Similar to hat we have done for the correlation coefficient, we can use a calculation tool to get the regression for theses columns. Since we want to predict the "Height" using the "Age", we have to use "Age" as the independent varible, "x", and "Height" as the dependent variable, "y".

Doing this, we get the regression equation:

`\hat{y}=0.117x+181.7`

(e) With the regression equation, we can predict the height of a player with age 26 by substituting 26 into "x":

`\begin{gathered} \hat{y}=0.117\cdot26+181.7 \\ \hat{y}=3.042+181.7 \\ \hat{y}=184.742\approx185 \end{gathered}`

So, the prediction of the equation is 185 cm.