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

Question

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

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

________________

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

Explanation / Answer

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:

Analysis of variance table for regression model:

Predicted values:

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

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

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