First, let's understand the relationship between the number of hours Jared studies and his test scores. Given the data:
[tex]\[
\begin{array}{|c|c|}
\hline
\text{Hours Studied} & \text{Test Score} \\
\hline
1 & 70 \\
\hline
2 & 75 \\
\hline
3 & 80 \\
\hline
\end{array}
\][/tex]
To find the logical conclusion on Jared's test score if he studies 4 hours, we need to determine the relationship between the number of hours studied and the test score. This can be achieved using linear regression, which provides us with an equation in the form \( y = mx + b \), where \( y \) is the predicted test score, \( x \) is the number of hours studied, \( m \) is the slope of the line, and \( b \) is the y-intercept of the line.
From the linear regression calculations:
- The slope (\( m \)) is 5.0.
- The y-intercept (\( b \)) is 65.0.
With these values, the linear equation that models Jared's test scores based on the hours he studied is:
[tex]\[
\text{Test Score} = 5 \cdot (\text{Hours Studied}) + 65
\][/tex]
Now, we want to predict the test score if Jared studies for 4 hours. Substituting 4 for \( x \) in the linear equation:
[tex]\[
\text{Test Score} = 5 \cdot 4 + 65 = 20 + 65 = 85
\][/tex]
Therefore, if Jared studies for 4 hours, his predicted test score is 85.
To determine the logical conclusion, we need to interpret this predicted score:
- Since 85 is greater than 80, the conclusion is:
- Jared will score higher than 80 on his test if he studies for 4 hours.
Thus, the final logical conclusion is:
C. He will score higher than 80 on his test.
