Problem #1 (71 pts) A is correlated to the score researcher wishes to determine

Question

Problem #1 (71 pts) A is correlated to the score researcher wishes to determine whether the score on a final sest in astatistics coune C) ce on the midterm (x1) and to the gender of the student (2-1 if male, otherwise) The wish multiple regression model was utilized for the midserm ( dis Data were collected on 15 stadents and utilized (10 pts) Complete the ANOVA a. table-MODEL1 Model Error Total 264.85 496.93 b. (9 pts) Conduct a test for the usefulness of the model. (I pts) Ho (3 pts) Test statistics: (2 pts) Rejection Region: (2 pts) Conclusion (check one): (1 pts) Interpretation (check one): vs Ha ?Reject Ho -Fail to Reject Ho There is statistical evidence to support Ha, the model is useful There is not enough statistical evidence to support Ha, the model is not useful (3 pts) The standard error of the model is equal to- c. - d. (21 pts) The parameter output for the multiple regression model above is provided here Variable Coeff t.err midtermm Gender 41.2 17.322380.0364 0.490.21233 0.0307 9.44 27.35 XXxx 0.7364 interaction0.14 0.32 044 XXXKx I. (6 pts) Compute the final score of John Mark, a student who scored 82 on his midterm TRUE FALSE TRUE FALSE TRUE FALSE TRUE FALSE I (15 pts) Answer the TRUE/FALSE questions (circle one) The t-test for the significance of Gender is equal to -0.35 The coefficient of midterm is equal to 11.09 The lower bound of the 95% confidence interval for Betal is approx.051 TRUE FALSE . The standard error of the coefficient of interaction is equal to 0.06 is meaninful to interpret the effect of gender

Explanation / Answer

a)

b) H0: Regression equation is not best fit to the given data
H1: Regression equation is best fit to the given data

Test Statistic F = 88.28/21.1 = 4.184

Rejection Region: F value > F critical value i.e. 3.5874

Conclusion: Reject H0
Since F value > F critical value

Correct answer: Option (A) the model is useful

c) Standard Error : sqrt(21.1) = 4.5935

d) i) Given John is male, Midterm = 82
Fianal score = 41.2 + 0.49 Midterm - 9.44 Gender + 0.14 Interaction
= 41.2 + 0.49 (82) - 9.44 (1) + 0.14 (82*1)
= 83.42
ii)

From the given data

t-test for gender = -9.44/27.35 = -0.35 true
Coefficient of midterm is equal to 11.09 false
false
false
false

ANOVA Table Source df Sum of square mean Square F-ratio Model 3 264.85 88.28 4.183886 Error 11 232.08 21.1 Total 14 496.93

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