First, it's important to understand what a least-squares regression line is. This line is used in statistics to describe the relationship between an independent variable (in this case, the mileage of a car) and a dependent variable (in this case, the price of a car). The equation of this line often takes the form:
[tex]\[ y = a + bx \][/tex]
where:
- [tex]\( y \)[/tex] is the predicted price of the car,
- [tex]\( x \)[/tex] is the number of miles,
- [tex]\( a \)[/tex] is the y-intercept (the price when the mileage is zero),
- [tex]\( b \)[/tex] is the slope of the line (the change in price for each additional mile driven).
Based on the data provided by the student using the computer output, the following coefficients were identified:
- The constant (intercept) is [tex]\( 24157.2 \)[/tex].
- The coefficient for Mileage (slope) is [tex]\( -0.181 \)[/tex].
Using these coefficients, we can write the equation of the least-squares regression line as follows:
[tex]\[ y = 24157.2 - 0.181x \][/tex]
This equation indicates that as the mileage of the car increases by one mile, the price of the car decreases by [tex]$0.181. The intercept value of 24157.2 suggests that if a car had zero miles, it would be predicted to be priced at $[/tex]24,157.20. Thus, the answer to the question about the equation of the least-squares regression line is:
[tex]\[ y = 24157.2 - 0.181x \][/tex]
Among the given options, this corresponds to the answer:
[tex]\[ y = 24157.2 - 0.181x \][/tex]
