Question

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

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

Homework Answers

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

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
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