Math Problem Statement

Call: lm(formula = final^(1.19) ~ log(finalfirst) + atndrte + finalfirst, data = marks)

Residuals: Min 1Q Median 3Q Max -31.582 -6.220 0.191 6.555 27.651

Coefficients: Estimate Std. Error t value (Intercept) 136.19258 46.41496 2.934 log(finalfirst) -61.01581 22.33493 -2.732 atndrte 0.13017 0.02845 4.576 finalfirst 4.02086 1.02948 3.906 Pr(>|t|)
(Intercept) 0.003499 ** log(finalfirst) 0.006522 ** atndrte 5.99e-06 *** finalfirst 0.000107 ***

Signif. codes:
0 ‘’ 0.001 ‘’ 0.01 ‘’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 9.803 on 496 degrees of freedom Multiple R-squared: 0.1902, Adjusted R-squared: 0.1853 F-statistic: 38.84 on 3 and 496 DF, p-value: < 2.2e-16 write the equation for the model

Solution

The regression model provided is:

final1.19^=136.19258+(61.01581)log(finalfirst)+0.13017atndrte+4.02086finalfirst\widehat{\text{final}^{1.19}} = 136.19258 + (-61.01581) \log(\text{finalfirst}) + 0.13017 \cdot \text{atndrte} + 4.02086 \cdot \text{finalfirst}

where:

  • final1.19\text{final}^{1.19} is the dependent variable (response variable),
  • log(finalfirst)\log(\text{finalfirst}) is the logarithm of the initial final-first score,
  • atndrte\text{atndrte} represents the attendance rate,
  • finalfirst\text{finalfirst} is the initial final-first score.

Would you like a detailed breakdown of the interpretation of each coefficient?

Related Questions:

  1. How do we interpret the coefficients in this model?
  2. Why is the response variable transformed using an exponent of 1.19?
  3. What does the multiple R-squared value tell us about the model?
  4. How does attendance rate (atndrte\text{atndrte}) impact the final score?
  5. What is the significance of the p-values in this regression output?

Tip:

When a model involves transformations (like exponentiation or logarithms), interpreting coefficients requires reversing the transformation to understand their effect in the original scale.

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Math Problem Analysis

Mathematical Concepts

Regression Analysis
Logarithms
Exponential Functions
Statistical Significance

Formulas

Regression model equation: final^(1.19) = 136.19258 + (-61.01581) log(finalfirst) + 0.13017 * atndrte + 4.02086 * finalfirst

Theorems

Interpretation of regression coefficients
Logarithmic transformations in regression

Suitable Grade Level

Grades 11-12