Question

What is the equation of the line of best fit that Shane drew? (Mathematics and Linear Regression) a) y = 5x + 10 b) y = 5x + 11 c) y = (1/5)x + 10

Answer 1

Without specific data or Shane's calculations, we cannot determine the exact line of best fit he drew. The general form for a regression equation is y = mx + b, but precise calculations require statistical methods or software.

Step-by-step explanation:

To answer the question, What is the equation of the line of best fit that Shane drew, we need additional specific information about the scatter plot or calculated values that Shane used. Without this information, we cannot accurately determine which equation represents the line of best fit that Shane drew. However, to create an equation for a line of best fit or least-squares regression line, one would typically start by plotting data points, drawing the best fit line by eye or using statistical software, then identifying two points on the line to calculate the slope (m), and finally determining the y-intercept (b) where the line crosses the y-axis. The regression equation would then have the form y = mx + b. For more precise predictions, statistical software can calculate a more accurate regression line using the least-squares method which minimizes the residuals or errors between the actual data points and the predicted values on the line.

Answer 2

The equation of the line of best fit drawn by Shane is y = 5x + 11.

Therefore, correct option is b) y = 5x + 11

Step-by-step explanation:

Shane's line of best fit is represented by the equation y = mx + b, where m is the slope and b is the y-intercept. To determine the equation, we need to identify the slope and y-intercept values.

The options are:

a) y = 5x + 10,

b) y = 5x + 11,

c)
`\(y = (1)/(5)x + 10\)`.

Shane's line of best fit has a slope of 5, which matches options a) and b). However, to determine the correct equation, we look at the y-intercept. Shane's line intersects the y-axis at y = 11, making the correct equation y = 5x + 11.

Therefore, the equation that best fits Shane's data is y = 5x + 11.

Linear regression in mathematics and how to determine the equation of the line of best fit.

Therefore, correct option is b) y = 5x + 11