Write R code to answer the quiz questions on Learn using the dataset below.

# 1 American Football Punters

## 1.1Description

Investigators studied physical characteristics and ability in 13 football punters. Each volunteer punted a football ten times. The investigators recorded the average distance for the ten punts, in feet. They also recorded the average hang time (time the ball is in the air before the receiver catches it) for the ten punts, in seconds. In addition, the investigators recorded five measures of strength and flexibility for each punter: right leg strength (pounds), left leg strength (pounds), right hamstring muscle flexibility (degrees), left hamstring muscle flexibility (degrees), and overall leg strength (foot-pounds). From the study “The relationship between selected physical performance variables and football punting ability” by the Department of Health, Physical Education and Recreation at the Virginia Polytechnic Institute and State University, 1983.

Variable        Description
-------------   --------------------------------
Distance        Distance travelled in feet
Hang            Time in air in seconds
R_Strength      Right leg strength in pounds
L_Strength      Left leg strength in pounds
R_Flexibility   Right leg flexibility in degrees
L_Flexibility   Left leg flexibility in degrees
O_Strength      Overall leg strength in pounds

Data File: ADA2_WS_01_punting.txt

## 1.2 Source

The Relationship Between Selected Physical Performance Variables and Football Punting Ability. Department of Health, Physical Education and Recreation, Virginia Polytechnic Institute and State University, 1983.

# 2 Rubric

1. Read the data set into R.
# First, download the data to your computer,
#   save in the same folder as this Rmd file.

str(punt)
'data.frame':   13 obs. of  7 variables:
$Distance : num 162 144 148 164 192 ...$ Hang         : num  4.75 4.07 4.04 4.18 4.35 4.16 4.43 3.2 3.02 3.64 ...
$R_Strength : int 170 140 180 160 170 150 170 110 120 130 ...$ L_Strength   : int  170 130 170 160 150 150 180 110 110 120 ...
$R_Flexibility: int 106 92 93 103 104 101 108 86 90 85 ...$ L_Flexibility: int  106 93 78 93 93 87 106 92 86 80 ...
$O_Strength : num 241 195 153 197 267 ... #punt 1. (7 p) Generate summaries summary() and frequency tables table() for each variable. Answer questions 1–7. # I'll get you started with the code, the rest is up to you. summary(punt)  Distance Hang R_Strength L_Strength Min. :104.9 Min. :3.020 Min. :110.0 Min. :110.0 1st Qu.:140.2 1st Qu.:3.640 1st Qu.:130.0 1st Qu.:130.0 Median :150.2 Median :4.040 Median :150.0 Median :150.0 Mean :148.2 Mean :3.921 Mean :147.7 Mean :143.8 3rd Qu.:163.5 3rd Qu.:4.180 3rd Qu.:170.0 3rd Qu.:160.0 Max. :192.0 Max. :4.750 Max. :180.0 Max. :180.0 R_Flexibility L_Flexibility O_Strength Min. : 85.00 Min. : 78.00 Min. :130.2 1st Qu.: 90.00 1st Qu.: 86.00 1st Qu.:153.9 Median : 93.00 Median : 93.00 Median :197.1 Mean : 95.69 Mean : 91.23 Mean :196.2 3rd Qu.:103.00 3rd Qu.: 94.00 3rd Qu.:240.6 Max. :108.00 Max. :106.00 Max. :266.6  apply(punt, 2, table) $Distance

104.93 105.67 117.59 140.25    144  147.5 150.17    162  162.5  163.5
1      1      1      1      1      1      1      1      1      1
165.17 171.75    192
1      1      1

$Hang 3.02 3.2 3.6 3.64 3.68 3.85 4.04 4.07 4.16 4.18 4.35 4.43 4.75 1 1 1 1 1 1 1 1 1 1 1 1 1$R_Strength

110 120 130 140 150 160 170 180
1   2   1   2   1   2   3   1

$L_Strength 110 120 130 140 150 160 170 180 2 1 2 1 3 1 2 1$R_Flexibility

85  86  89  90  92  93  95 101 103 104 106 108
1   1   1   1   2   1   1   1   1   1   1   1

$L_Flexibility 78 80 83 86 87 92 93 94 95 106 1 1 1 1 1 1 3 1 1 2$O_Strength

130.24 132.68 152.99 153.92 154.64 195.49 197.09 205.88 219.25 240.57
1      1      1      1      1      1      1      1      1      2
260.56 266.56
1      1 

Note that you can do even better than reading the numbers from above to answer the specific quiz questions. Instead, you can (not required) write code that returns the specific values you want. For example:

* The minimum distance is 104.93 ft.
1. (2 p) Plot $$y=$$Distance and $$x=$$Hang and interpret the plot in terms of linearity and strength of correlation.
# plot distance by hang
library(ggplot2)
# p <- ggplot(punt, aes(x = , y = ))
# ...
# print(p)
1. (2 p) Calculate the Pearson correlation between Distance and Hang (read the help for performing the hypothesis test). Answer questions 8–9.

2. (2 p) Create a new categorical (factor) variable, O_StrengthFac, from the quantitative variable overall leg strength (O_Strength) to indicate high leg strength: code less than 200 as 0 (low leg strength) and at least 200 as 1 (high leg strength).

# create categorical variable

Plot $$y=$$Distance and $$x=$$O_StrengthFac and interpret the comparison of distance by strength group.

# plot distance by strength group
library(ggplot2)
# p <- ggplot(punt, aes(x = , y = ))
# ...
# print(p)
1. (2 p) Use a two-sample $$t$$-test (assume equal variance) to test whether $$H_0: \mu_{\textrm{low}} = \mu_{\textrm{high}}$$, that the population means for distance are equal for the two overall leg strength groups you created. Answer questions 10–11.

2. (2 p) Plot $$y=$$Distance and $$x=$$R_Flexibility and interpret the relationship.

library(ggplot2)
# p <- ggplot(punt, aes(x = , y = ))
# ...
# print(p)
1. (2 p) Regress $$y=$$Distance on $$x=$$R_Flexibility. Answer questions 12–13.

2. (2 p) Create a new variable which is the mean of the right leg and left leg flexibility variables, O_Flexibility. Generate a frequency distribution for this new variable. Answer questions 14–15.