Math Problem Statement

fill in the blank

What is the value of s_e? (Round your answer to five decimal places)

Solution

To calculate the value of ses_e, which represents the standard error of the estimate (the standard deviation of the residuals), we can use the formula:

se=(yiyi^)2n2s_e = \sqrt{\frac{ \sum (y_i - \hat{y_i})^2 }{n - 2}}

Where:

  • yiy_i are the observed values (the percentages of salmon transported),
  • yi^\hat{y_i} are the predicted values from the regression equation, and
  • nn is the number of data points (in this case, the number of rows of data).

From the Minitab output:

  • R2=83.2%R^2 = 83.2\%, and
  • The residual standard error S=9.16217S = 9.16217.

The residual standard error SS is actually the value of ses_e, which represents the standard error of the estimate.

So, the value of ses_e is:

se=9.16217s_e = 9.16217

Please confirm if you need additional details or clarifications. Here's a list of related questions that might help deepen understanding:

  1. What is the interpretation of the coefficient for the total number of salmon in the regression equation?
  2. How do you calculate the predicted percentage of salmon transported for a given total number using the regression equation?
  3. How does the R2R^2 value reflect the quality of the regression model?
  4. What does it mean if the standard error of the estimate is large or small in a regression analysis?
  5. How do residuals impact the validity of a regression model?

Tip: Always check whether the assumptions of linear regression (such as linearity, independence, and homoscedasticity) hold before drawing conclusions from the regression model.

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Math Problem Analysis

Mathematical Concepts

Regression Analysis
Standard Error of the Estimate
Least Squares Method

Formulas

s_e = sqrt(sum((y_i - hat{y_i})^2) / (n - 2))

Theorems

Least Squares Estimation

Suitable Grade Level

Grades 10-12