Mission 4_Questions

STAT E-100 FA 2023 Mission 4 You are a researcher who is interested in exploring whether there is a relationship between how much of a certain type of exercise a person can do. 1. A broad jump is a calisthenics, cardiovascular, and plyometrics exercise that primarily targets the quads and to a lesser degree also targets the calves, hamstrings and hip flexors. The sit-up (or curl-up ) is an abdominal endurance training exercise to strengthen, tighten and tone the abdominal muscles . Use R to generate a scatterplot with sit_ups_counts on the X-axis (horizonal axis) and broad_jump_cm as the Y-axis (vertical axis). Include the R code used to generate the visualization. plot(x = bodyPerformance$sit_ups_counts, y = bodyPerformance$broad_jump_cm, pch = 19, col = " lightblue ") 2. In the scatterplot generated in question 1), is the correlation positive, negative, or zero? Based on findings from the shape or pattern of the visualization alone, how do you know? The correlation is positive because the line of best fit is closer to a slope of 1 than -1 3. Use R to calculate the sample covariance between sit_ups_counts and broad_jump_cm . Include the R code used to generate the value. Include the units of measurement for each variable. cov(x = bodyPerformance$sit_ups_counts, y =

STAT E-100 FA 2023 Mission 4 bodyPerformance$broad_jump_cm) The unit of measurement for situps is amount of sit ups and for the broad jump it’s cm . 425.9025 4. Calculate the sample standard deviation of sit_ups_counts and broad_jump_cm using R. Include the R code used to generate the values. Include the units of measurement for each variable. Sit ups are measured in sit ups completed and the br oad jump is measured in cm > sd ( bodyPerformance$sit_ups_counts ) [1] 14.2767 sit ups > sd ( bodyPerformance$broad_jump_cm ) [1] 39.868 cm 5. Calculate the value of the sample correlation coefficient through the formula below. Use the sample standard deviation of sit_ups_counts , the sample standard deviation of broad_jump_cm, and the sample covariance between sit_ups_counts and broad_jump_cm . Indicate a) whether the sample correlation coefficient is strong, weak, or non-existent using the rubric below this question, b) whether it is positive, negative, or near zero. Note: ❑ ❑ 6. Use R to generate the sample correlation coefficient value for sit_ups_counts and broad_jump_cm using the cor() function. Include the R code used. The value should match the value from question 5. > cor (x = bodyPerformance$sit_ups_counts , y = bodyPerformance$broad_jump_cm ) [1] 0.7482728 7. We will be taking steps to convert a person’s height of 160 cm into a z-score statistic. You may use Excel, R Studio, or pen and paper. The steps are: a. Calculate the sample mean ( x̄ ) for height_cm. 168.5598cm