Question

1. You have data on two variables: exam score and student preparation time for the exam in hours. You collect data from 6 students. (8 Points)

Student Exam Prep Time (hours) Exam Score

Student	Exam Prep Time (hours)	Exam Score
1	2	61
2	6	92
3	9	95
4	4	80
5	5	78
6	3	68

a. What will be the dependent variable and the independent variable?

b. Construct a Scatter Plot.

c. What type of relationship do the two variables have?

d. Compute the values for ?0 and ?1.   

e. Write the estimated regression equation.

f. Calculate the r2 and r.

g. What is the predicted test score if a student does not prepare for the exam at all?

h. How would you interpret ?1 (saying that it is the slope is not sufficient)

Answer 1

a. Here independent variable is Exam Preparation Time and dependent variable is Exam Score

b.

c. We see the increasing trend in the scatter graph hence it is positive correlation between x and y

d.

Sum of X = 29
Sum of Y = 474
Mean X = 4.8333
Mean Y = 79
Sum of squares (SS_X) = 30.8333
Sum of products (SP) = 152

Regression Equation = ŷ = bX + a

= SP/SS_X = 152/30.83 = 4.9297
= M_Y - bM_X = 79 - (4.93*4.83) = 55.1730
e. ŷ = 4.9297X + 55.1730

f.

X Values
∑ = 29
Mean = 4.833
∑(X - M_x)² = SS_x = 30.833

Y Values
∑ = 474
Mean = 79
∑(Y - M_y)² = SS_y = 872

X and Y Combined
N = 6
∑(X - M_x)(Y - M_y) = 152

R Calculation
r = ∑((X - M_y)(Y - M_x)) / √((SS_x)(SS_y))

r = 152 / √((30.833)(872)) = 0.927

So r^2=0.859

g. For x=0, y==55.1730

h. For every increase in x, y will have a constant change in y and that value is slope