Question

In a recent survey concerning ages and annual income, 4 people responded with the information in the table below. Suppose that the best-fit line obtained for this data is ŷ = 3.07x -43.47, where age is the independent variable.

a) Find the estimated values of y and the residuals for the data points.
For full marks your answer should be accurate to at least two decimal places.

name	age	Annual income(thousands)	Estimated value	Residual
irlene	46	94.1	0	0
siran	50	113.3	0	0
wasim	48	103.8	0	0
wynn	20	18.4	0	0

b) Compute the sum of squared errors.
For full marks your answer should be accurate to at least two decimal places.

SSE = 0

Answer 1

a)

The solution is :

name	age	Annual income(thousands)	Estimated value ŷ = 3.07x -43.47	Residual ei = y - ŷ
irlene	46	94.1	97.75	-3.65
siran	50	113.3	110.03	3.27
wasim	48	103.8	103.89	-0.09
wynn	20	18.4	17.93	0.47

Here estimated value ŷ = 3.07x -43.47 is calculated by plugging the value of x. For example:

For irelene, it will be 3.07 * 46 - 4.347 = 97.75

The Residual is the difference between the observed and calculated value.For example:

For irelene, it will be 94.1-97.75 = -3.65

b)

SSE = 24.2444

The calculations are:

name	age	Annual income(thousands)	Estimated value ŷ = 3.07x -43.47	Residual ei = y - ŷ	Residual^2 ei = (y - ŷ)^2
irlene	46	94.1	97.75	-3.65	13.3225
siran	50	113.3	110.03	3.27	10.6929
wasim	48	103.8	103.89	-0.09	0.0081
wynn	20	18.4	17.93	0.47	0.2209
					24.2444

Just square residuals and take their sum.

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