Question

1. (a) Plot four different points whose y coordinates are half their -coordinates. Do these points lie on a line? If so, what is the equation of the line?

(b) Plot the points (1, -1), (2, -2), (3, -3), (4, -4) on the same graph. These points all lie on a line. What is the equation of this line?
2. Find the regression equation for predicting final score from midterm score, based on the following information.
a. average midterm score = 70, SD = 10
b. average final score = 48, SD = 20, r ~ 0.70
3. A researcher wants to use a straight line to predict income from height, for a large group of residents of a certain state. There is a weak positive association in the data. True or false, and explain
(a)He can use many different lines.
(B)He has to use the regression line.
(C)Only the regression line has an r.m.s. error.
(D)Any line he uses will have an r.m.s. error.
(E)Among all lines, the regression line has the smallest r.m.s. error.

Answer 1

In part (a), we plot four different points with y coordinates half their x coordinates and find the equation of the line. In part (b), we plot the points (1, -1), (2, -2), (3, -3), and (4, -4) and find the equation of the line.

Step-by-step explanation:

1. (a) To plot four different points whose y coordinates are half their x coordinates, we can choose any x value and find the corresponding y value. For example, if we choose x = 2, then y = 2/2 = 1. So, one of the points will be (2, 1). Similarly, we can choose other x values and find their corresponding y values to plot the points.

After plotting the points, we can see that they lie on a line. The equation of this line can be found by finding the slope and y-intercept using any two points on the line. Let's take the points (2, 1) and (4, 2):

The slope, m, can be calculated as (change in y)/(change in x) = (2-1)/(4-2) = 1/2.

Using the point-slope form, y - y1 = m(x - x1), and substituting the values of (x1, y1) = (2, 1) and m = 1/2, we get the equation y - 1 = 1/2(x - 2).

(b) The points (1, -1), (2, -2), (3, -3), and (4, -4) all lie on a line. To find the equation of this line, we can again find the slope and y-intercept using any two points. Let's take the points (1, -1) and (4, -4):

The slope, m, can be calculated as (change in y)/(change in x) = (-4-(-1))/(4-1) = -3/3 = -1.

Using the point-slope form, y - y1 = m(x - x1), and substituting the values of (x1, y1) = (1, -1) and m = -1, we get the equation y + 1 = -1(x - 1).

Therefore, the equation of the line is y = -x.