Answered

Get personalized answers to your unique questions on IDNLearn.com. Get timely and accurate answers to your questions from our dedicated community of experts who are here to help you.

A collection of paired data consists of the number of years that students have studied Spanish and their scores on a Spanish language proficiency test. A computer program was used to obtain the least squares linear regression line, and the computer output is shown below. Along with the paired sample data, the program was also given an [tex]$x$[/tex] value of 2 (years of study) to be used for predicting test score.

Equation:
[tex]\[ y = mx + b \][/tex]

Statistics:
- [tex]$r^2 = 0.83$[/tex]
- [tex]$r = 0.91$[/tex]

Parameters:
- [tex][tex]$m = 10.90$[/tex][/tex]
- [tex]$b = 31.55$[/tex]

Question:
If a person studies 4.5 years, what is the single value that is the best predicted test score? Assume that there is a significant linear correlation between years of study and test score.
(1 point)

Sagot :

GinnyAnsweridn
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.
Thank you for using this platform to share and learn. Don't hesitate to keep asking and answering. We value every contribution you make. Find clear answers at IDNLearn.com. Thanks for stopping by, and come back for more reliable solutions.