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).

Question

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.

类似问题

Below are the results of an association study conducted by Saha, Morris and Kang (2019):Adjusted R2 = 0.689 Which of the following is incorrect?

Question8 Including irrelevant regressors in multiple regression typically: Select one alternative: a) Increases variance of estimates b) Biases coefficients c) Reduces variance of estimates d) Leaves [math] unchanged ResetMaximum marks: 0.5 Flag question undefined

In the multiple regression model, [math: yi=β1+β2xi+β3zi+ui]y_i=\beta _1+\beta _2x_i +\beta _3z_i+u_i, which of the following leads to improved precision on the estimates [math: β^2]\hatβ_2, (that is, smaller [math: se(β^2|x,z)]se(\hat{\beta}_2|x,\,z)?[Fill in the blank]

What is the consequence of including irrelevant variables (those that have no direct effect on the dependent variable) in your regression model?[Fill in the blank]

Question at position 19 Cause-and-Effect Models can have multiple independent variables.TrueFalse

更多留学生实用工具

智能学习助手

风格化写作助手

论文查重助手

文献引用助手

课堂转译助手

课堂笔记助手

Quiz搜索助手

学校历年真题

智能刷题助手

智能匹配练习

希望你的学习变得更简单