Question

The average number of people in a family that received welfare for various years is given below.

Year	Welfare family size
1969	4.0
1973	3.6
1975	3.2
1979	3.0
1983	3.0
1988	3.0
1991	2.9

Part (a)

Calculate the least squares line. Put the equation in the form of:

? = a+ bx.

(Round your answers to three decimal places.)
? = ________ + _______ x

Part (b)

Find the estimated welfare family size in 1972. (Use your equation from part (a). Round your answer to one decimal place.)
people
_______________
Find the estimated welfare family size in 1989. (Use your equation from part (a). Round your answer to one decimal place.)
people

________________

Answer 1

The statistical software output for this problem is:

Simple linear regression results:
Dependent Variable: Welfare family size
Independent Variable: Year
Welfare family size = 88.720616 - 0.043176816 Year
Sample size: 7
R (correlation coefficient) = -0.85326872
R-sq = 0.72806751
Estimate of error standard deviation: 0.23287573

Parameter estimates:

Parameter	Estimate	Std. Err.	Alternative	DF	T-Stat	P-value
Intercept	88.720616	23.362318	? 0	5	3.7975947	0.0127
Slope	-0.043176816	0.01180077	? 0	5	-3.6588136	0.0146

Analysis of variance table for regression model:

Source	DF	SS	MS	F-stat	P-value
Model	1	0.72598732	0.72598732	13.386917	0.0146
Error	5	0.27115554	0.054231108
Total	6	0.99714286

Predicted values:

X value	Pred. Y	s.e.(Pred. y)	95% C.I. for mean	95% P.I. for new
1972	3.5759354	0.12662773	(3.2504285, 3.9014424)	(2.894534, 4.2573369)
1989	2.8419296	0.14055165	(2.4806301, 3.2032291)	(2.1427225, 3.5411366)

Hence,

Part a):

? = 88.721 + (-0.043) x

Part b):

Estimated welfare family size in 1972 = 3.6

Estimated welfare family size in 1989 = 2.8