Question

1. The superintendent of a school district wanted to predict the percentage of students passing a sixth-grade proficiency test. She obtained the data on percentage of students passing the proficiency test (% Passing), mean teacher salary in thousands of dollars (Salaries), and instructional spending per pupil in thousands of dollars (Spending) of 47 schools in the state. Following is the multiple regression output with Y=% Passing as the dependent variable, X1=Salaries and X2=Spending. Regression Statistics Multiple R 0.4276 R Square 0.1828 Adjusted R Square 0.1457 Standard Error 5.7351 Observations 47 ANOVA df SS MS F Significance F Regression 2 323.8284 161.9142 4.9227 0.0118 Residual 44 1447.2094 32.8911 Total 46 1771.0378 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept -72.9916 45.9106 -1.5899 0.1190 -165.5184 19.5352 Salary 2.7939 0.8974 3.1133 0.0032 0.9853 4.6025 Spending 0.3742 0.9782 0.3825 0.7039 -1.5972 2.3455

          1. The superintendent of a school district wanted to predict the percentage of students passing a sixth-grade proficiency test. She obtained the data on percentage of students passing the proficiency test (% Passing), mean teacher salary in thousands of dollars (Salaries), and instructional spending per pupil in thousands of dollars (Spending) of 47 schools in the state. Following is the multiple regression output with Y=% Passing as the dependent variable, X1=Salaries and X2=Spending.

Regression Statistics
Multiple R 0.4276
R Square 0.1828
Adjusted R Square 0.1457
Standard Error 5.7351
Observations 47

ANOVA
df SS MS F Significance F
Regression 2 323.8284 161.9142 4.9227 0.0118
Residual 44 1447.2094 32.8911
Total 46 1771.0378

Coefficients Standard Error t Stat P-value Lower 95% Upper 95%
Intercept -72.9916 45.9106 -1.5899 0.1190 -165.5184 19.5352
Salary 2.7939 0.8974 3.1133 0.0032 0.9853 4.6025
Spending 0.3742 0.9782 0.3825 0.7039 -1.5972 2.3455

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1. The superintendent of a school district wanted to predict the percentage of students passing a sixth-grade proficiency test. She obtained the data on percentage of students passing the proficiency test (% Passing), mean teacher salary in thousands of dollars (Salaries), and instructional spending per pupil in thousands of dollars (Spending) of 47 schools in the state. Following is the multiple regression output with Y=% Passing as the dependent variable, X1=Salaries and X2=Spending.

Regression Statistics
Multiple R 0.4276
R Square 0.1828
Adjusted R Square 0.1457
Standard Error 5.7351
Observations 47

ANOVA
df SS MS F Significance F
Regression 2 323.8284 161.9142 4.9227 0.0118
Residual 44 1447.2094 32.8911
Total 46 1771.0378

Coefficients Standard Error t Stat P-value Lower 95% Upper 95%
Intercept -72.9916 45.9106 -1.5899 0.1190 -165.5184 19.5352
Salary 2.7939 0.8974 3.1133 0.0032 0.9853 4.6025
Spending 0.3742 0.9782 0.3825 0.7039 -1.5972 2.3455

Added by Laura G.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

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Solved by Expert Sri K

02/11/2023

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The multiple regression output provides information about the relationship between the dependent variable (% Passing) and the independent variables (Salaries and Spending). Show more…

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1. The superintendent of a school district wanted to predict the percentage of students passing a sixth-grade proficiency test. She obtained the data on percentage of students passing the proficiency test (% Passing), mean teacher salary in thousands of dollars (Salaries), and instructional spending per pupil in thousands of dollars (Spending) of 47 schools in the state. Following is the multiple regression output with Y=% Passing as the dependent variable, X1=Salaries and X2=Spending. Regression Statistics Multiple R 0.4276 R Square 0.1828 Adjusted R Square 0.1457 Standard Error 5.7351 Observations 47 ANOVA df SS MS F Significance F Regression 2 323.8284 161.9142 4.9227 0.0118 Residual 44 1447.2094 32.8911 Total 46 1771.0378 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept -72.9916 45.9106 -1.5899 0.1190 -165.5184 19.5352 Salary 2.7939 0.8974 3.1133 0.0032 0.9853 4.6025 Spending 0.3742 0.9782 0.3825 0.7039 -1.5972 2.3455

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00:01 This question we are given here value of n so we are given here data so we are given n which is equal to 21 and s which is equal to we are given here 5 .7 so these two value we are given here 5 .7 and here that value of n sample size now highotidist hypothesis test here we have hypothesis test for the hypothesis test so here we can make sigma which is equal to 5 .5 which is this h1 which is equal to sigma greater than 5 .1 now that the chai test here we have chai square test chai square test for the chai just chai square test the df which is equal we can write is n minus 1 which is equal to 21 minus 1 which is equal to we can write 20 so this is value of df now critical value here you can write critical value which is equal to we can write 31 .410 so this is our critical value here this is our critical value now i explain here let's write the explanation so here suppose we have t statistics here we have t statistics equal we can write n minus 1 1 by here as square divided by we can write sigma square which is a substitute value so we can write 21 minus 1 here we can write 517 square divided by we can write here 5 .1 square now again we just simplify and we can write here answer is 24 .983 980 this is our test statistics now here the critical value of greater than the taste value take a value is greater than test value so we have failed to reject the null hypothesis here for fail to reject the null hypothesis null hypothesis and here the insufficient evidence and here the insufficient evidence that conclude the standard evidence evidence of the ages of 3 that hg is 0 .5 .1.

02:40 So here we have taste value.

02:43 This is our taste value here.

02:46 Now reject here.

02:48 Fail to reject null hypothesis...

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