A student would like to know if the time spent on studying and number of lectures attended for an exam is related to the exam scores. The student now collects data on the number of lectures attended in the same period. The information obtained is tabulated and the output from a multiple regression analysis is shown below: We want to test whether the number of lectures attended makes a contribution to the regression model. What is the p-value for the test? Answer: Answer Question 6[input] (Please provide your answer to 4 decimal places).

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BlackTom AI · Accepted Answer

To determine whether the number of lectures attended contributes to the regression model, we test the null hypothesis that the coefficient for 'Number of lectures attended' equals zero.

First, inspect the regression output for the coefficient corresponding to 'Number of lectures attended'. The table shows:
- Coefficient: 5.24
- Standard Error: 4.45
- t Stat: 1.179938
- p-value: 0.260883

Next, interpret the t statistic and p-value. The t statistic measures how many standard errors the estimated coefficient is away from zero. A small absolute t value indicates the coefficient is not significantly different from zero. In this case, |t| ≈ 1.18, which is modest in size given the degrees of freedom.

The p-value represents the probability of observing such a t statistic (or more extreme) if the null hypothesis were true (coefficient = 0). A p-value of approximately 0.2609 means there is about a 26% chance of obtaining this t value by random variation alone when the true effect is zero.

A conventional significance level (e.g., α = 0.05) would require p ≤ α to declare significance. Since 0.2609 > 0.05, we do not reject the null hypothesis. Therefore, based on this regression output, the number of lectures attended does not provide a statistically significant contribution to the model at the 5% level.

Additional context: the degrees of freedom for the residual are listed as 12 (df = 12 for residual), which corresponds to the sample size minus the number of parameters estimated. The relatively large standard error (4.45) compared to the coefficient (5.24) also contributes to the non-significance.

In summary, the p-value for the test of the lectures-attended coefficient is 0.2609, indicating no statistically significant contribution at common significance levels.

ETX5900 - S2 2025 Take Home Quiz Week 10 (due on 17th of October)

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