Question

how does the pattern of the residuals about this line compare with the pattern of the data points about the regression line in your scatterplot from part (a)? y - r
f) below is given a table of the data set, x, y, predicted y and residuals. in this table there are some missing numbers (let them be a, b and c). find these numbers and show work.

speed (x)	10	20	30	40	50	60	70	80
fuel (y)	38.1	54.0	68.4	63.6	60.5	55.4	50.6	c
predict $hat{y}$	55.1	54.87	a	54.41	54.19	53.96	53.73	53.5
residual (y - $hat{y}$)	-17	-0.87	13.76	b	6.31	1.44	-3.13	-9.70

g) say in words what the numerical value of the slope tells you.

Explanation:

Step1: Find value of A

Residual = Observed Y - Predicted Y. For the row with X = 30, we know Observed Y = 68.4 and Residual = 13.76. So, Predicted Y (A) = Observed Y - Residual.
$A=68.4 - 13.76=54.64$

Step2: Find value of B

For the row with X = 40, Observed Y = 63.6 and Predicted Y = 54.41. Residual (B) = Observed Y - Predicted Y.
$B=63.6 - 54.41 = 9.19$

Step3: Find value of C

For the row with X = 80, Predicted Y = 53.5 and Residual=-9.70. Observed Y (C) = Predicted Y+Residual.
$C=53.5+( - 9.70)=43.8$

Answer:

$A = 54.64$, $B = 9.19$, $C = 43.8$