Question

question 3 (5 points)
use the given data to find the best predicted value of the response variable.
based on the data from six students, the regression equation relating number of
hours of preparation (x) and test score (y^) is \\( \hat { y } = 67.3 + 1.07 x \\). the
same data yield r = 0.224 and \\( \overline { y } = 75.2 \\).
what is the best predicted test score for a student who spent 2 hours preparing for
the test?
69.4
59.7
78.1
75.2
question 4 (5 points)
use the given data to find the equation of the regression line. round the final values
to three significant digits, if necessary.
ten students in a graduate program were randomly selected. their grade point
averages (gpas) when they entered the program were between 3.5 and 4.0. the
following data were obtained regarding their gpas on entering the program versus
their current gpas.
entering gpa current gpa
3.5 3.6
3.8 3.7
3.6 3.9
3.6 3.6

Explanation:

Step1: Substitute \(x = 2\) into the regression equation

Given the regression equation \(\hat{y}=67.3 + 1.07x\), when \(x = 2\), we have \(\hat{y}=67.3+1.07\times2\).

Step2: Calculate the value of \(\hat{y}\)

First, calculate \(1.07\times2 = 2.14\). Then, \(67.3+2.14=69.44\approx69.4\).

Answer:

69.4