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:
where:
- is the dependent variable (response variable),
- is the logarithm of the initial final-first score,
- represents the attendance rate,
- is the initial final-first score.
Would you like a detailed breakdown of the interpretation of each coefficient?
Related Questions:
- How do we interpret the coefficients in this model?
- Why is the response variable transformed using an exponent of 1.19?
- What does the multiple R-squared value tell us about the model?
- How does attendance rate () impact the final score?
- 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