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
(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 |
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