Teacher is assessing the correlation between the number of hours spent studying and the average score on a science test. the table shows the data:

number of hours spent studying
(x) 0 0.5 1 1.5 2 2.5 3 3.5 4
score on science test
(y) 57 62 67 72 77 82 87 92 97

part a: is there any correlation between the number of hours students spent studying and the score on the science test? justify your answer. (4 points)

part b: write a function that best fits the data. (3 points)

part c: what does the slope and y-intercept of the plot indicate? (3 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.