Question

A statistics professor would like to build a model relating student scores on the first test to the scores on the second test. The test scores from a random sample of 21 students who have previously taken the course are given in the table. Test Scores Student First Test Grade Second Test Grade 1 86 78 2 47 61 3 95 82 4 53 66 5 69 74 6 97 86 7 59 66 8 45 62 9 44 60 10 45 65 11 50 69 12 88 78 13 76 74 14 61 69 15 73 72 16 75 77 17 73 70 18 42 64 19 62 68 20 67 68 21 43 60 Step 1 of 2 : Using statistical software, estimate the parameters of the model Second Test Grade=β0+β1(First Test Grade)+εi. Enter a negative estimate as a negative number in the regression model. Round your answers to 4 decimal places, if necessary.

Answer 1

Using regression equation from Excel, the output be

44.7703132368825 F18 K H G D B A Test score First Test Grade Second Test Grade 78 SUMMARY OUTPUT 86 1 61 47 2 Regression Statistics 82 95 3 0.9515 Multiple R 66 53 4 0.9054 R Square 74 69 0.9004 Adjusted R Square 86 97 6 2,2981 Standard Error 66 59 7 21 Observations 62 45 60 44 ANOVA 65 45 10 Significance F F MS df SS 69 50 11 0.0000 181.8970 960.6119 960.6119 1 Regression 78 88 12 5.2811 19 100.3404 Residual 74 76 13 1060.9524 20 Total 61 69 14 72 73 15 Upper 95% Lower 95% P-value t Stat Standard Error Coefficients 77 75 16 48.8168 40.7238 0.0000 23.1572 1.9333 44.7703 Intercept 70 73 17 0.4525 0.3309 13.4869 0.0000 0.0290 0.3917 First Test Grade 64 42 18 68 62 19 68 67 20 60 43 21

The estimated value of ;$\beta _{0}$ is 44.7703 (Intercept)

The estimated value of $\beta _{1}$ is 0.3917 (Slope)

The regression equation is Second Grade Student (Y) = 44.7703 + 0.3917*First Grade student

Slope = 0.3917 which is >0 therefore, First grade student and second grade student is positive correlation

As First grade student score increase 1 mark then second grade student score is also increase 0.3917 mark

The p-value of the slope is 0.000 which is less than alpha 0.05 so we conclude that the regression equation is best fit to the given data

R² = 0.9054 = 90.54% of the variation in the second grade student  is explained by the independent variable "First grade student"