The administrator of a school board was analyzing the average mathematics test scores in the schools under her control.

3. The administrator of a school board was analyzing the average mathematics test scores in the schools under her control. She wondered whether the dramatic differences in mathematics test scores among the schools was related to the percentage of teachers in each school who had Maths degrees, the mean age of the Maths teachers and the average annual income of the Maths teachers. She took a random sample of 40 schools and produced the following Excel output. SUMMARY OUTPUT Regression Statistics Multiple R 0.597 R Square 0.857 Adjusted R Square 0.3 03 Standard Error 7.724 Observations 40 df MS F Significance F Regression 3 1192.732 897.577 6.663 3E-04 Residual 36 2148.058 59.668 Total 39 3340.791 Coefficients Standard Error t Stat P-value Intercept 2.367 7.278 4.901 2E-05 Math Degree 0.201 0.069 3.543 0.001 Age 0.216 0.185 1.321 0.388 Income 0.102 0.152 0.872 0.004 a) Construct the equation of the regression line. b) Assess the fit of the model using the standard error (Se ) and the coefficient of determination (RZ ) c) Assess the validity of the model using Hypothesis Testing at a 5% level of significance. What are the Null and Alternate Hypotheses?What is the value of p and the meaning for H1 and Ho? State the conclusion in sentence form [i.e. whether or not the model is valid] d} Conduct Hypothesis Tests for the variables. What are the Null and Alternate Hypotheses for of the variables? For each variable, indicate the pvalue, the meaning for H1 and Ho VARIABLE PVALUE MEANING FOR H1. and Ho State the overall conclusion {i.e., the relationship ofthe variables} in sentence form