Question

The table below gives the number of hours ten randomly selected students spent studying and their corresponding midterm exam grades. Using this data, consider the equation of the regression line, y = bo + b1x, for predicting the midterm exam grade that a student will earn based the number of hours spent studying. Keep in mind, the correlation coefficient may or may not be statistically significant for the data given. Remember, in practice, it would not be appropriate to use the regression line to make a prediction if the correlation coefficient is not statistically significant.

Hours Studying 0 1 1.5 2 2.5 3 4.5 5 5.5 6
Midterm Grades 65 70 77 79 83 91 92 94 95 98
a. Find the estimated slope. Round your answer to three decimal places.
b. Find the estimated y-intercept. Round your answer to three decimal places.
c. Find the estimated value of y when x=5. Round your answer to three decimal places.
d. Find the error prediction when x=2. Round your answer to three decimal places.

Answer 1

Explanation:

Given is a table of values of x and y.

X represents the number of hours ten randomly selected students spent studying and Y their corresponding midterm exam grades.

x y

0 65

1 70

1.5 77

2 79

2.5 83

3.4 91

5 92

5 94

5.5 95

6 98

Correlation 0.973459204

Since correlation is near to 1, there is a linear association and hence regression linear line can be fitted.

a)
`slope = 5.273`

b)
`y intercept = 67.579`

c)
`Regression line is y = 5.273x+67.579`

Substitute x =5

`y(5) = 5.273(5)+67.579\\=93.944`

d) when x =2

`y(2) = 78.125`

Actual value for x=2 is 79

Error = Actual - estimated

=
`79-78.125\\=0.875`