In Exercises 3 and 7, we asked you to make and describe a scatterplot for the hiker data shown in the table. \begin{tabular}{lrrrrrrrr} \hline Body weight (lb) & 120 & 187 & 109 & 103 & 131 & 165 & 158 & 116 \\ Backpack weight (Ib) & 26 & 30 & 26 & 24 & 29 & 35 & 31 & 28 \\ \hline \end{tabular} 1. Calculate the equation of the least-squares regression line. 2. Make a residual plot for the linear model in Question 1. 3. What does the residual plot indicate about the appropriateness of the linear model? Explain your answer.
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To find the least-squares regression line, we need to calculate the slope (\(b\)) and the y-intercept (\(a\)) of the line using the formulas: \[ b = \frac{n(\sum xy) - (\sum x)(\sum y)}{n(\sum x^2) - (\sum x)^2} \] \[ a = \frac{\sum y - b(\sum x)}{n} \] Where: - Show more…
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Refer to your graph from Exercise 5. (a) Describe the relationship between body weight and backpack weight for this group of hikers. (b) One of the hikers is a possible outlier. Identify the body weight and backpack weight for this hiker. How does this hiker affect the form of the association?
Describing Relationships
Scatterplots and Correlation
10. Suppose that we are interested in predicting weight of students based on height. We have run a regression analysis with the resulting estimated regression equation as follows: "The estimated weight equals (-180 pounds) plus (5 pounds times the height in inches)." a. Suppose that one student is 3 inches taller than another student. What is the estimated difference in weight? b. Suppose that a given student is 65 inches tall. What is the estimated weight? c. Suppose that the regression equation above was based on a sample of students ranging in height from 60 to 75 inches. Now estimate the height of a 48-inch-tall student. Comment. d. Explain clearly the meaning of the 5 in the equation above. e. Explain clearly the meaning of the -180 in the equation above.
Kari H.
The following data represent the heights and weights of a random sample of professional baseball players. Player Height (in inches) Weight (pounds) Alex Rodriguez 75 225 Derek Jeter 75 195 Greg Maddux 72 180 Randy Johnson 82 231 Orlando Cabrera 69 185 Angel Sanchez 74 190 Ken Griffey, Jr. 75 228 Marlon Anderson 71 200 Rounding your final answer to one decimal place, if a player has a height of 76 inches, what would we predict as the player's weight?
Jerelyn N.
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