Questions: Identify the values of the y-intercept a and the slope b, and sketch the following regression lines for values of x between 0 and 10. Complete parts (a) through (d). a. Find a and b for the equation y-hat=1+0.2x. a=1 b=.2 Sketch the regression line y-hat=1+0.2x, for values of x between 0 and 10. b. Find a and b for the equation y-hat=1+x. a= square b= square

Identify the values of the y-intercept a and the slope b, and sketch the following regression lines for values of x between 0 and 10. Complete parts (a) through (d).
a. Find a and b for the equation y-hat=1+0.2x.
a=1 b=.2

Sketch the regression line y-hat=1+0.2x, for values of x between 0 and 10.
b. Find a and b for the equation y-hat=1+x.
a= square b= square

Transcript text: Identify the values of the $y$-intercept a and the slope $b$, and sketch the following regression lines for values of $x$ between 0 and 10. Complete parts (a) through (d). a. Find a and b for the equation $\hat{y}=1+0.2 \mathrm{x}$. \[ a=1 \quad b=.2 \] Sketch the regression line $\hat{y}=1+0.2 x$, for values of $x$ between 0 and 10. b. Find a and b for the equation $\hat{y}=1+\mathrm{x}$. \[ a=\square \quad b=\square \]

Solution

Solution Steps

Step 1: Identify the y-intercept (a) and the slope (b) for the equation ŷ = 1 + 0.2x

The given equation is ŷ = 1 + 0.2x.
The y-intercept (a) is the constant term, which is 1.
The slope (b) is the coefficient of x, which is 0.2.

Step 2: Sketch the regression line for ŷ = 1 + 0.2x for values of x between 0 and 10

To sketch the regression line, we need to plot the line using the y-intercept and the slope.
When x = 0, ŷ = 1.
When x = 10, ŷ = 1 + 0.2(10) = 1 + 2 = 3.
The line passes through the points (0, 1) and (10, 3).

Step 3: Choose the correct graph

The correct graph should show a line starting at y = 1 when x = 0 and ending at y = 3 when x = 10.
Among the given options, graph A correctly represents this line.