Math Problem Statement

The data below represent the number of days​ absent, x, and the final​ grade, y, for a sample of college students at a large university. Complete parts​ (a) through​ (e) below. No. of​ absences, x 0 1 2 3 4 5 6 7 8 9

Final​ grade, y 89.3 86.5 83.5 81.1 78.1 73.8 64.5 68.8 65.9 63.1 Question content area bottom Part 1 ​(a) Find the​ least-squares regression line treating the number of​ absences, x, as the explanatory variable and the final​ grade, y, as the response variable. ModifyingAbove y with caretequals    enter your response herexplusleft parenthesis nothing right parenthesis    ​(Round to three decimal places as​ needed.)

Solution

The least-squares regression line, treating the number of absences xx as the explanatory variable and the final grade yy as the response variable, is given by:

y^=89.3043.076x\hat{y} = 89.304 - 3.076x

Where y^\hat{y} is the predicted final grade, and xx is the number of absences.

Do you need any further details or have any questions?

Here are five related questions:

  1. How can you interpret the slope of the regression line?
  2. What does the intercept represent in this context?
  3. How would you predict the grade for a student with 5 absences using this model?
  4. What is the significance of the R2R^2 value in this regression analysis?
  5. How can outliers affect the least-squares regression line?

Tip: Always check the residuals to assess how well your regression model fits the data!

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Math Problem Analysis

Mathematical Concepts

Statistics
Linear Regression
Correlation

Formulas

y = b0 + b1x (Least-squares regression line)
Slope formula: b1 = Σ[(x - mean_x)(y - mean_y)] / Σ(x - mean_x)^2

Theorems

Least-Squares Method
Linearity in Regression

Suitable Grade Level

College Level