Professor
a Statistics Professor Investigated Some of the Factors That $$y = \beta _ { 0 } + \beta _ { 1 } x _ { 1 } + \beta _ { 2 } x _ { 2 } + \beta _ { 3 } x _ { 3 } + \epsilon$$

question 82

Short Answer

Professor
A statistics professor investigated some of the factors that affect an individual student's final grade in his course.He proposed the multiple regression model $$y = \beta _ { 0 } + \beta _ { 1 } x _ { 1 } + \beta _ { 2 } x _ { 2 } + \beta _ { 3 } x _ { 3 } + \epsilon$$ where:
y = final mark (out of 100)
x₁ = number of lectures skipped
x₂ = number of late assignments
x₃ = mid-term test mark (out of 100)
The professor recorded the data for 50 randomly selected students.The computer output is shown below. The regression equation is:
$$\hat { y } = 41.6 - 3.18 x _ { 1 } - 1.17 x _ { 2 } + .63 x _ { 3 }$$
$\begin{array}{l|lll|}\hline \text { Predictor } & \text { Coef } & \text { StDev } & T \\\hline \text { Constant } & 41.6 & 17.8 & 2.337 \\x_{1} & -3.18 & 1.66 & -1.916 \\x_{2} & -1.17 & 1.13 & -1.035 \\x_{3} & 0.63 & 0.13 & 4.846 \\\hline\end{array}$
$$S = 13.74$$
$$\mathrm { R } - \mathrm { Sq } = 30.0 \%$$
Analysis of Variance
$\begin{array}{l|llll}\hline \text { Source of Variation } & \text { df } & \text { SS } & M S & F \\\hline \text { Regression } & 3 & 3716 & 1238.667 & 6.558 \\\text { Error } & 46 & 8688 & 188.870 & \\\hline \text { Total } & 49 & 12404 & & \\\hline\end{array}$
-Do these data provide enough evidence to conclude at the 5% significance level that the final mark and the number of skipped lectures are linearly related?
Test statistic = ____________________
Critical Value = ____________________
Conclusion: ____________________

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Definitions:

Truth Table

A mathematical table used in logic to compute the functional values of logical expressions on each of their functional arguments.

Statement Form

An expression using statement variables and connectives to state the logical form of an actual or possible statement.

Conditional

Involving or implying a condition in logic or mathematics, often expressed in "if... then..." statements that assert the dependency of one event or outcome on another.

Tautology

In logic, a statement that is true in every possible interpretation or a redundant expression that doesn't add informational value.