Question Type 4: Choosing the appropriate data given contextual information Exercises

Person A collected data on weekly junk food servings and average idle heart rate for 20 weeks but weeks 5, 12 and 17 have missing heart rate readings. How many complete weeks remain for analysis?

Person A has recorded the following variables over 10 weeks:\n• Weekly junk food servings: [3, 5, 4, 6, 7, 5, 4, 8, 2, 6]\n• Daily screen time (hours): [2, 3, 2.5, 4, 3.5, 3, 2, 4.5, 2, 3]\n• Average idle heart rate (bpm): [70, 72, 69, 71, 73, 70, 68, 74, 67, 71]\nWhich of these variables should Person A include to investigate the effect of weekly junk food consumption on average idle heart rate, and why?

Given 18 weeks of data, Person A wants only the most recent 12 weeks. If the data is labeled week 1 through 18, write the mathematical expression to select the subset for analysis.

From the cleaned dataset of 15 weeks, the weekly junk food servings are [3,5,4,6,7,5,4,8,2,6,5,4,7,6,5]. Calculate the mean and standard deviation of junk food servings.

Over 12 weeks, Person A’s weekly junk food servings are [4, 5, 6, 100, 5, 6, 7, 5, 4, 6, 5, 120]. Identify and remove outliers in this series using the IQR method.

Using the regression line $y=0.83x+66.54$, predict the average idle heart rate for a subject consuming 10 servings of junk food in a week.

Using the 15-week cleaned dataset of garbage servings and idle heart rate below, compute the Pearson correlation coefficient $r$.\nWeekly junk food servings (x): [3,5,4,6,7,5,4,8,2,6,5,4,7,6,5] \nIdle heart rate (y): [70,72,69,71,73,70,68,74,67,71,70,69,73,72,70]

After selecting the last 12 weeks, Person A notices one value of weekly junk food servings is zero. Discuss whether this is an outlier in context and how you would decide to keep or remove it.

To smooth weekly junk food servings, Person A applies a 3-week moving average on the series [3,5,4,6,7,5,4,8,2,6]. Compute the smoothed values for weeks 2–9.

Fit a least-squares regression line $y = mx + c$ predicting idle heart rate from weekly junk food servings using the 15-week dataset in question 5. Compute $m$ and $c$.

Test whether the slope $m=0.83$ of the regression line is significantly different from zero at $\alpha=0.05$ given $t = m/SE_m = 0.83/0.15 = 5.53$ with 13 degrees of freedom.

Person A also recorded weekly exercise hours. Explain how weekly exercise could act as a confounding variable when analyzing the relationship between junk food consumption and idle heart rate, and suggest a mathematical method to adjust for it.