Question

Data was collected from students to determine the effects on overall grade average and number of hours spent playing video games per week.

Grade   Hours/Week
20 23
96 3
74 6
85 5
67 8
56 14
79 4
65 7
Which is the:
-Independent variable?   _______________________
-Dependent variable?   _______________________

-Calculate the coefficient of correlation and interpret the results.

-Determine both the coefficient of determination and non-determination and explain the result.

-Determine the unrounded regression equation for this data set.

-Using the regression equation predict the grade average when 15 hours are played per week. Show all work involved in finding your answer.

Answer 1

Independent variable = Hours/Week
Dependent variable = Grade

The coefficient of correlation:

Table 1:

Table 2:

Use this formula to calculate the Correlation Coefficient:

So, the correlation coefficient is -0.965.

Interpretation:

It means there is a negative correlation between Hours/Week and Grade. When students playing video games hours per week then the students Grand will decrease.

The coefficient of determination:

Take the Sqaure of Correlation Coefficient

r = -0.965

r square = = 0.9312 or we can write 93.12%

The non-determination:

1-0.9312 = 0.0688 or we can write 6.88%

The unrounded regression equation:

From above Table 2 :

Where m is the Slope and n is the intercept of our regression equation:

Now predict the Grade from given Hours/Week = 15

Y = 96.809 - 3.321 * 15

Y = 96.809 - 49.815

Y = 46.994

So when a student spent 15 Hours/Week then the Grade will be 46.994 from Regreesion Equation.