Question

solve the problem using your calculator. 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 (x) and their current gpas (y). use linear regression to find a linear function that predicts a student’s current gpa as a function of his or her entering gpa. entering gpa: 3.5, 3.8, 3.6, 3.5, 3.9, 4.0, 3.9, 3.5, 3.7, entries current gpa: 3.6, 3.7, 3.9, 3.6, 3.9, 3.8, 3.7, 3.9, 3.8, 4.0. options: a. ( y = 4.91 + 0.0212x ); b. ( y = 2.51 + 0.329x ); c. ( y = 5.81 + 0.497x ); d. ( y = 3.67 + 0.0313x )

Explanation:

To find the linear regression equation \( y = a + bx \) (where \( x \) is Entering GPA and \( y \) is Current GPA), we can use a calculator or software (like a TI - 84 Plus or Excel) to perform linear regression on the given data.

Step 1: Input the data

We have the following pairs of (Entering GPA, Current GPA):
\((3.5, 3.6)\), \((3.8, 3.7)\), \((3.6, 3.9)\), \((3.5, 3.6)\), \((3.9, 3.9)\), \((3.8, 3.8)\), \((4.0, 3.7)\), \((3.9, 3.9)\), \((3.5, 3.8)\), \((3.7, 4.0)\)

Step 2: Calculate the regression coefficients

Using a calculator (for example, in a TI - 84 Plus:

1. Press STAT then EDIT and enter the Entering GPA values in L1 and Current GPA values in L2.
2. Press STAT then CALC then LinReg(ax + b).
3. Select L1 as the Xlist and L2 as the Ylist, then calculate.

After performing the linear regression, we find that the equation of the line of best fit (linear regression equation) is \( y=2.51 + 0.329x\) (when we calculate the slope \( b\) and the y - intercept \( a\) from the data).

Answer:

B. \( y = 2.51+0.329x\)