To determine the predicted test score for someone who has studied Spanish for 4.5 years, we need to use the given linear regression equation: [tex]\(y = mx + b\)[/tex].
Here's a step-by-step solution:
1. Identify the parameters from the given equation:
- The slope ([tex]\(m\)[/tex]) of the regression line: 10.90
- The y-intercept ([tex]\(b\)[/tex]) of the regression line: 31.55
2. Identify the given number of years of study:
- [tex]\(x\)[/tex] (years of study) = 4.5
3. Substitute the values into the linear regression equation:
- The equation is [tex]\(y = mx + b\)[/tex]
- Substitute [tex]\(m = 10.90\)[/tex], [tex]\(b = 31.55\)[/tex], and [tex]\(x = 4.5\)[/tex] into the equation.
4. Calculate the predicted score by substituting these values into the equation:
[tex]\[
y = 10.90 \times 4.5 + 31.55
\][/tex]
5. Simplify the calculation:
[tex]\[
y = 49.05 + 31.55
\][/tex]
[tex]\[
y = 80.60
\][/tex]
Therefore, the best predicted test score for a person who has studied Spanish for 4.5 years is 80.60.
