Question

⃝c Jim Stallard 2019: Reproduction, in whole or in part, requires written consent of the copyright holder.4

MINITAB output:

Pearson correlation of MATScore and CalculusGrade = 0.840
Coefficients

Term       Coef  SD Coef  T-Value  P-Value
Constant  40.78     8.51     4.79    0.001
MATScore  0.766    0.175     4.38    0.002

⃝c Jim Stallard 2019: Reproduction, in whole or in part, requires written consent of the copyright holder.5

1. (a) From the scatterplot, what can you say about the relationship between a student’s math achievement

   test score and their Calculus I final grade?

2. (b) Letting a student’s math achievement test score be the predictor variable x and their Calculus I final grade by the response variable y, estimate the model that allows you to predict a student’s Calculus I final grade as a linear function of his/her math achievement test score.

3. (c) Find the coefficient of determination, and interpret its meaning.

4. (d) Does the data indicate that the y-intercept of the model can be removed or retained? Use a level of significance of 5%.

5. (e) Find a 95% confidence interval estimate for β1, and interpret its meanign. (Note: t0.025,df=8 = 2.306).

6. (f) Consider the following MINITAB output:

        Variable  Setting
        MATScore       70
   

            Fit   SE Fit        95% CI              95% PI
        94.3735  5.02118  (82.7946, 105.952)  (71.2024, 117.545)
   

   Find a 95% confidence interval that will predict the Calculus I final grade of a student who scored 70% on their math achievement test score.

Answer 1

(a) Since Scatter plot is missing however Pearson correlation of MATScore and CalculusGrade = 0.840 which indicates that there is a linear relationship between a student’s math achievement test score and their Calculus I final grade and the direction is positive and strength of relation is fairly good.

(b)

i.e. 70.56% of total variation in the sample of student's Calculus I final grade is explained by their math achievement test score through this regression equation.

(d) Since p-value of y-intercept=0.001<0.05 so there is sufficient evidence that the y-intercept of the model is different from zero hence this can be retained.

(e) 95% confidence interval estimate for β1 is

(0.766- 2.306 *0.175, 0.766+ 2.306 *0.175)=(0.3625, 1.1696)

Hence we are 95% confident that true value of β1 lies between 0.3625 and 1.1696.

(f) 95% confidence interval that will predict the Calculus I final grade of a student who scored 70% on their math achievement test score=( 71.2024, 117.545)