Question

The table below gives the number of hours five randomly selected students spent studying and their corresponding midterm exam grades. Using this data, consider the equation of the regression line, yˆ=b0+b1x, for predicting the midterm exam grade that a student will earn based on 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 2 4 5

Midterm Grades 67 77 83 97 99

Answer 1

The hypothesis being tested is:

H0: ρ = 0

Ha: ρ ≠ 0

x	y
0	67
1	77
2	83
4	97
5	99
r²	0.976
r	0.988
Std. Error	2.411
n	5
k	1
Dep. Var.	y

Pearson's r is 0.988.

The critical r-value is 0.878.

Since 0.988 > 0.878, we can reject the null hypothesis.

Therefore, we can conclude that the correlation coefficient is statistically significant.

The equation of the regression line is:

y = 69.1395 + 6.4419*x