Question

DISPLAY A Descriptives Descriptive Statistics N Minimum Maximum Mean Std. Deviation 1.376 72.673 EXPENDITURE 48 3.656 9.774 5.946 SAT 48 854.000 1107.000 970.563 Valid N (listwise) 48 Model Summary Model R R Square Adjusted R Std. Error of Square the Estimate 65.492 453 205 188 a Predictors: (Constant), EXPENDITURE ANOVA Model F Sig. Sum of df Mean Square Squares 50920.77 11.872 0.001 4289.197 1 Regression 50920.77 1 Residual 197303.00 46 Total 248223.80 47 a Predictors: (Constant), EXPENDITURE b Dependent Variable: SAT Coefficients Unstandardized Standardized t Sig Coefficients Beta Coefficients Model B Std. Error 1 (Constant) 1112.769 42.341 -23.918 6.942 26.28 000 -0.453 -3.45 001 EXPEND a Dependent Variable: SAT 3. A school dis such as the SAT. school performance, including expenditures for education an Displays A below shows some of the key results from this analysis researcher would like to study the relationship between the amount of money a trict spend on education, and the performance of students on a standardized test Data was obtained for 48 states on several variables associated with d SAT performance. Write the estimated regression equation for the whole class, and interpret the sample intercept and slope coefficient values. a. 1150 1100 1050 1000 950 900 a50 800 9 10 3 Expendture par pup b. Draw the estimated regression line for the sample onto the plot given here. c. Comment on the appropriateness of the regression model, from both a substantive and statistical perspective. (e.g, is the math test a good predictor of science performance for the whole class (boys and girls together)? Is using this model the best way to predict science performance?) Wherever possible, refer to output and specific statistics to support your answer. ol district is arguing that they would like to increase their expenditures on d. A scho students to be at the average expenditure for the 48 states of this data set the predicted SAT score for students in a school with an average expenditure? . What would be

Answer 1

Solution:

Part A:

The estimated Regression equation is:

SAT = 1112.769 - 23.918 Expend

Part B:

1150 1112.769 1100 1050 1000 SAT= 1112.769-23.918 Expend 950 900 850 800 10 Expenditure per pup

Part C:

The regression model is not a good fit this is because... The value of R² is not close to 1. The value is 0.205 which means that only 20.5% of the variations in the dependent variables are explained by the independent variables which doesn't signifies a good fit...

The value of significance F in the Anova table is 0.001 which is less than 0.05.. This means that the model is statistically significant which is a good sign..

Part D:

The regression equation is:

SAT = 1112.769 - 23.918 Expend

Expend will be at at the average of the 48 states = 5.946

So, SAT = 1112.769 - 23.918 * 5.946

So, SAT = 970.5

So, by increasing the expenditure by the average of 48 states will generate a SAT score of 970.5.

End of the Solution..