Question

The average number of people in a family that received welfare for various years is given below. (Source: House Ways and Means Committee, Health and Human Services Department)

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

• Use “year” as the independent variable and “welfare family size” as the dependent variable, Answer from your excel sheet:

• a) Calculate the least squares line. Put the equation in the form of: y=a-bx. To 2 decimal places with a 0 in front of the decimal if needed.

• b) Find the correlation coefficient to 2 decimal places.

• c) Use http://www.socscistatistics.com/pvalues/pearsondistribution.aspx to calculate the P value with significance level 0.05. Round to 3 decimal places.

• d) Is it significant?

• yes/no

• e) Based on the above data, is there a linear relationship between the year and the average number of people in a welfare family? Yes/no

• f) What is the estimated average welfare family size for 1986 using a)? Round to 1 decimal places.

• g) Does the least squares line give an accurate estimate for 1960 or 1995? yes/no

Answer 1

(a) y = 88.72 - 0.04*x

(b) r = -0.85

(c) The p-value is 0.015.

(d) yes

(e) yes

(f) 3.0

(g) no

	r²	0.728
	r	-0.853
	Std. Error	0.233
	n	7
	k	1
	Dep. Var.	Size
ANOVA table
Source	SS	df	MS	F	p-value
Regression	0.7260	1	0.7260	13.39	.0146
Residual	0.2712	5	0.0542
Total	0.9971	6
Regression output				confidence interval
variables	coefficients	std. error	t (df=5)	p-value	95% lower	95% upper
Intercept	88.72
Year	-0.04	0.0118	-3.659	.015	-0.0735	-0.0128