Data Set 6-9
The correlation between high school GPA and college GPA is .50. Given the data that follow, your task is to predict college GPA.
$$\begin{array} { l c c c }
& \underline{ \text { College GPA } } & \underline{ \text { High School GPA} } \
\text { Mean } & 2.6 & 3.3 & \
\text { Standard Deviation } & 0.5 & 0.7
\end{array}$$
-Look at Data Set 6-9. For a person with a high school GPA of 2.5, the predicted college GPA is
A) 2.04
B) 2.31
C) 2.88

Question

Data Set 6-9
The correlation between high school GPA and college GPA is .50. Given the data that follow, your task is to predict college GPA.
 $$\begin{array} { l c c c } 
&  \underline{ \text { College GPA } } & \underline{ \text { High School GPA} } \
\text { Mean } & 2.6 & 3.3 & \
\text { Standard Deviation } & 0.5 & 0.7
\end{array}$$
-Look at Data Set 6-9. For a person with a high school GPA of 2.5, the predicted college GPA is
A) 2.04
B) 2.31
C) 2.88

Quizplus · Accepted Answer

The prediction of college GPA from high school GPA can be made using the formula for a regression line, which is often stated as $Y' = a + bX$, where $Y'$ is the predicted score, $a$ is the intercept, $b$ is the slope, and $X$ is the score from which we are predicting. The slope $b$ can be calculated using the formula $b = r(\sigma_Y / \sigma_X)$, where $r$ is the correlation between the two variables, $\sigma_Y$ is the standard deviation of the outcome variable (college GPA), and $\sigma_X$ is the standard deviation of the predictor variable (high school GPA). The intercept $a$ can be calculated using the formula $a = \bar{Y} - b\bar{X}$, where $\bar{Y}$ and $\bar{X}$ are the means of the outcome and predictor variables, respectively.Given:- $r = 0.50$- $\sigma_Y = 0.5$- $\sigma_X = 0.7$- $\bar{Y} = 2.6$- $\bar{X} = 3.3$First, calculate $b$:$$b = 0.50 \times \frac{0.5}{0.7} = 0.357$$Then, calculate $a$:$$a = 2.6 - (0.357 \times 3.3) = 1.4239$$Finally, predict the college GPA for a high school GPA of 2.5:$$Y' = 1.4239 + (0.357 \times 2.5) = 1.4239 + 0.8925 = 2.3164$$Rounded to two decimal places, the predicted college GPA is 2.31.

Data Set 6-9 the Correlation Between High School GPA and College

Data Set 6-9
the Correlation Between High School GPA and College