Math Problem Statement
Suppose you have the following data:
x 1 2 3 4 5 6
y 24 29 28 42 33 41
and the LSRL is ŷ =21.73+3.171x Find the residual value for x = 1.
Solution
To calculate the residual value for , we use the formula for residuals:
-
Step 1: Find the observed value when .
From the given data, when , . -
Step 2: Find the predicted value using the least squares regression line (LSRL) equation:
Substitute into the equation:
- Step 3: Calculate the residual:
Thus, the residual value for is -0.901.
Let me know if you'd like further clarification on any step!
Related Questions:
- How do you calculate the residual for other values of ?
- What does a negative residual indicate about the fit of the regression line?
- How do you calculate the sum of squared residuals (SSR)?
- What is the significance of residual analysis in regression?
- How does the residual help in understanding the model's performance?
Tip:
Residuals help identify patterns that might indicate the model's weaknesses. If residuals show a non-random pattern, it may suggest that the linear regression model is not the best fit for the data.
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Math Problem Analysis
Mathematical Concepts
Linear Regression
Residuals
Least Squares Regression Line (LSRL)
Formulas
Residual = y_observed - y_predicted
ŷ = 21.73 + 3.171x
Theorems
Least Squares Regression Method
Suitable Grade Level
Grades 9-12