Asked by Julannah Cobbs on May 06, 2024
Verified
A researcher is investigating variables that might be associated with the academic performance of high school students.She examined data from 1990 for each of the 50 states plus Washington,DC.The data included information on the following variables. As part of her investigation,she ran the multiple regression model SATM = 0 + 1($ per pupil) + 2(% taking) + i,
Where the deviations i were assumed to be independent and Normally distributed with a mean of 0 and a standard deviation of .This model was fit to the data using the method of least squares.The following results were obtained from statistical software. Suppose we wish to test the hypotheses H0: 1 = 2 = 0 versus Ha: at least one of the j is not 0,using the ANOVA F test.What is the value of the F statistic?
A) 3.32
B) 24.0
C) 79.65
D) 159.3
Multiple Regression
A method in statistics for analyzing how a dependent variable's variation is explained by two or more independent variables.
Academic Performance
The extent to which a student, teacher, or institution has achieved their short or long-term educational goals.
ANOVA F Test
A statistical test used in ANOVA (Analysis of Variance) to determine if there are any statistically significant differences between the means of three or more independent groups.
- Ascertain the relevance of variables in regression models by conducting hypothesis tests.
Verified Answer
From the ANOVA table, we have SSR = 1898.96, SSE = 2667.23, p = 3, and n = 51. Substituting these values into the formula, we get F = (1898.96/3) / (2667.23/47) = 79.65. The p-value for this F statistic is less than 0.001, indicating strong evidence against the null hypothesis H0, and in favor of the alternative hypothesis Ha. Therefore, we conclude that at least one of the coefficients j is not zero, and that the model is a good fit for the data.
Learning Objectives
- Ascertain the relevance of variables in regression models by conducting hypothesis tests.
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