Question

Two variables, x and y are linearly related. The regression equation of yon x is

y = 3.5+2.3x. One data point used to construct this regression equation is

(5,17.5). What is the residual for this point and is the predicted value for x = 5

too small or too large?

OA. 15, too small

OB. 2.5, too large

O C. -2.5, too small

OD. -2.5, too large

E. 2.5, too small

Answer 1

The residual for the data point (5, 17.5) using the regression equation y = 3.5+2.3x is 2.5, indicating that the predicted value was too small.

Step-by-step explanation:

The student asked for the residual of a data point (5,17.5) when the regression equation given is y = 3.5+2.3x. To find the residual, we calculate the predicted y value using x = 5 in the equation, which gives us y = 3.5 + 2.3(5) = 3.5 + 11.5 = 15. However, the actual y value given is 17.5. The residual is the difference between the actual value and the predicted value, hence 17.5 - 15 = 2.5. Since the actual value is greater than the predicted value, the prediction was too small. Therefore, the correct answer is 2.5, too small.

Answer 2

To find the residual for the point (5,17.5), you calculate the predicted y using the regression equation, compare it to the actual y, and judge if the prediction is too small or too large. The residual is 2.5, indicating the predicted value is too small.

Step-by-step explanation:

The question asks to find the residual for the data point (5,17.5) using the given regression equation y = 3.5 + 2.3x and to determine if the predicted value for x = 5 is too small or too large. First, we need to calculate the predicted value for y when x = 5:

• y = 3.5 + 2.3(5)
• y = 3.5 + 11.5
• y = 15

The predicted value of y for x = 5 is 15. The actual given y value for x = 5 is 17.5.

The residual is the difference between the actual y value and the predicted y value:

• Residual = actual y - predicted y
• Residual = 17.5 - 15
• Residual = 2.5

Since the residual is positive, the predicted value was too small. Therefore, the correct answer is 2.5, too small.