On the first day of class, an economics professor administers a test to gauge the math preparedness of her students. Shebelieves that the performance on this math test and the number of hours studied per week on the course are the primaryfactors that predict a student's score on the final exam. Using data from her class of 60 students, she estimates A portion of the regression results is shown in the following table.a. What is the slope coefficient of Hours?b. What is the sample regression equation?c. What is the predicted final exam score for a student who has a math score of 70 and studies 4 hours per week? **Transcription for Educational Website**---**Understanding Regression Analysis in Education**Consider a scenario where an economics professor aims to evaluate the math preparedness of her students with an initial test. She hypothesizes that performance on this math test and the number of hours studied per week are crucial factors predicting a student’s score on the final exam. Therefore, she models the final exam score as follows:\[ \text{Final} = \beta_0 + \beta_1 \text{Math} + \beta_2 \text{Hours} + \epsilon. \]Using data from her 60 students, the professor estimates the following regression results:### Regression Results Table| | **Coefficients** | **Standard Error** | **t Stat** | **p-value** ||--------------|------------------|--------------------|------------|---------------|| **Intercept**| 40.55 | 3.37 | 12.03 | 2.83E-17 || **Math** | 0.25 | 0.04 | 6.06 | 1.14E-07 || **Hours** | 4.85 | 0.57 | 8.53 | 9.06E-12 |**Analysis Questions:**a. **What is the slope coefficient of Hours?** - The slope coefficient of Hours is **4.85**. This indicates that for each additional hour studied per week, the final exam score is expected to increase by 4.85 points, assuming other factors are constant.b. **What is the sample regression equation?** - The sample regression equation is: \[ \text{Final} = 40.55 + 0.25 \times \text{Math} + 4.85 \times \text{Hours}. \]c. **What is the predicted final exam score for a student who has a math score of 70 and studies 4 hours per week?** - Using the regression equation: \[ \text{Predicted Final} = 40.55 + 0.25 \times 70 + 4.85 \times 4. \] - Calculation: \[ \text{Predicted Final} = 40.55 + 17.5 + 19.4 = 77.45.

The table shows the regression output.a) From the table, it is clear that the slope coefficient of hours is 4.85.Thus, the slope coefficient of hours is 4.85.b) The intercept value (b0) is 40.55.The slope coefficient of Math (b1) is 0.25 and the slope coefficient of hours (b2) is 4.85.The general regression equation is Final =b0+b1(Math)+ b2(Hours).Thus, the regression equation is:Final = 40.55+0.25 Math +4.85 Hoursc) The predicted final exam score for a student who has a math score of 70 and studies 4 hours per week is:Thus, the predicted final exam score for a student who has a math score of 70 and studies 4 hours per week is 77.45.a) The slope coefficient of hours is 4.85.b) The regression equation is:Final = 40.55+0.25 Math +4.85 Hoursc) The predicted final exam score for a student who has a math score of 70 and studies 4 hours per week is 77.45.