Question

Question 3: Evaluate this model with the global test at the significance level a 0.05. (6 points) Step 1: State the hypotheses H1: Step 2: Compute the global F-statistic for the model. (Round to the nearest 100) Step 3: Find F-value for the critical value. (Round to the nearest 100) Step 4: State decision rule Step 5: State a conclusion and interpret the conclusion. Table 2 presents the parameter estimates of the regression model. Conduct a test of Question 4: the regression coefficients individually at the significance level of 0.05. Conclude which variable(s) is(are) useful in explaining the variation in Calculus grade. You are required to state the reasoning for your conclusion. Hint: the p-value approach can be used. (2 points) Table 2: Parameter Estimates Variable Intercept Algebra grade 0.961 ATC math ATC science HS rank Coefficients Standard Error Statistic p-value 36.122 0.272 0.216 0.135 10.752 0.264 0.454 3.36 3.64 0.60 0.69 01.31 0.001 0.001 0.551 0.492 0.196 0.313 0.104

Answer 1

1)

a)

DF for regression =no. of predictors = 4

b)

DF for residuals=N-no. of predictors-1 = 80-4-1=75

2)

a) MSR=SSR/DF= 2986.15 / 4 = 746.538
b) MSE=SSE/DF = 7346.05 /75 = 97.947

3)

Anova table
variation	SS	df	MS	F-stat
regression	2986.15	4	746.538	7.6218
error,	7346.05	75	97.947
total	10332.20	79

step 1      
Ho: overall regression model is not significant      
H1: overall regression model is significant      
      
step 2      
      
F-stat=MSR/MSE =    7.62  
      
step 3      
F-critical value = 2.49 (using F-table ,alpha=0.05,df=4,75)
      
step 4-      
|F-stat|>f-critical ,then reject Ho, otherwise not      

step 5          
since F-stat > F-critical , so, rejct Ho   
hence, overall regression model is significant.

4)

for variable algebra,p-value=0.001 < alpha=0.05

so, it is significantly different from zero

for variable ATC math,p-value=0.0551>alpha=0.05, so, not significnat

fir variable ATC science,p-value = 0.492>alpha=0.05,s0 not significant

for variable, HS rank, p value=.0.196>alpha=0.05,so also not significant

so, only algebra grade is significant in explaining the variation on calculus grade