Josh is preparing for an exam by completing practice tests that have different numbers of questions. for each practice test he notes the number of questions and the time it takes him to complete the the test. next josh creates a scatter plot and draws a trend line to fit the data. to see how well the trend line represents the data, josh draws black lines to represent the distance each data point lies away from the trend line. what is the sum of the residuals for all the points?

answer-

the sum of the residuals for all the points is 0

solution-

while doing a regression analysis our objective is to find a line of best fit. usually all the data points don’t lie exactly on this regression equation line. they are scattered around the line.

a residual represents the difference or variation between the actual or observed value and the predicted value. on the graph, it is the vertical distance between a data point and the regression line.

they are positive if they lie above the regression line and negative if they lie below the regression line. if the regression line actually passes through the point, the residual at that point is zero, i.e the observed value is same as the predicted value.

if the line is actually the line of best fit, then sum of the residuals and their mean is equal to zero.

the options to this answer are:

a. 97

b. 58

c. 19

d. 39

i believe the answer is 19 but i'm not 100% sure. correct be if i'm wrong! have a super day anyways!