Math Problem Statement
The following data represent commute times (in minutes) and scores on a well-being survey. Complete parts (a) through (d). Commute Time (minutes), x 5 15 30 40 50 72 105
Well-Being Index Score, y 69.0 67.6 65.8 64.9 64.0 62.6 58.8 Question content area bottom Part 1 (a) Find the least-squares regression line treating the commute time, x, as the explanatory variable and the index score, y, as the response variable. ModifyingAbove y with caretequals negative 0.097xplusleft parenthesis 69.074 right parenthesis (Round to three decimal places as needed.) Part 2 (b) Interpret the slope and y-intercept, if appropriate. First interpret the slope. Select the correct choice and, if necessary, fill in the answer box to complete your choice. A. For every unit increase in index score, the commute time falls by enter your response here, on average. (Round to three decimal places as needed.) B. For a commute time of zero minutes, the index score is predicted to be enter your response here. (Round to three decimal places as needed.) C. For every unit increase in commute time, the index score falls by enter your response here, on average. (Round to three decimal places as needed.) D. For an index score of zero, the commute time is predicted to be enter your response here minutes. (Round to three decimal places as needed.) E. It is not appropriate to interpret the slope.
Solution
Let's begin by calculating the least-squares regression line based on the provided data.
Step 1: Least-Squares Regression Line
The general form of the least-squares regression line is:
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Math Problem Analysis
Mathematical Concepts
Linear Regression
Statistics
Correlation
Formulas
Least-squares regression line formula: ŷ = b0 + b1x
Theorems
Least-Squares Theorem
Slope-Intercept Form
Suitable Grade Level
Grades 10-12
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