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 (b) Calculate the least squares line. Put the equation in the form of: ? = a + bx. (Round your answers to three decimal places.)

? = +   x

Part (g) Using the rounded least squares line, estimate the welfare family sizes for 1960 and 1995. (Use your equation from part (b). Round your answer to one decimal place.)

1960 ( )	people
1995 ( )	people

Does the least squares line give an accurate estimate for those years? Explain why or why not.

Yes, we can estimate the welfare family size for any year using the least squares line.No, the years are outside the domain of 1969 to 1991.     

Part (h) Are there any outliers in the above data?

Yes, (1969, 4.0) is an outlier.

Yes, (1991, 2.9) is an outlier.     

Yes, (1969, 4.0) and (1991, 2.9) are outliers.

No, there are no outliers.

Part (i) What is the estimated average welfare family size for 1987? (Use your equation from part (b). Round your answer to one decimal place.)

( ) people

Part (j) What is the slope of the least squares (best-fit) line? (Round your answer to three decimal places.)

( )

Answer 1

(b)

X                       Y              XY                X²

1969             4.0                7876           3876961

1973             3.6              7102.8          3892729

1975            3.2               6320             3900625

1979            3.0               5937               3916441

1983          3.0               5949            3932289

1988            3.0             5964             3952144

1991           2.9             5773.9           3964081

-------------------------------------------------------------------------

13858        22.7           44922.7         27435270

Least square line is:

(c)

(i)

For x = 1960:

For x = 1995:

(ii)

Correct option:

No, the years are outside the domain of 1969 to 1991.

(h)

Outlier test:

Arranging data inascending order, we get:

2.9,3.0,3.0,3.0,3.2,3.6,4.0

So,

Q1 = 3.0

Q3 = 3.6

IQR = 3.6 - 3.0 = 0.6

Low side: Q1 - 1.5 IQR = 3.0 - (1.5 X 0.6) = 2.1

So, no outlier on Low Side

High side : Q3 + 1.5 IQR = 3.6 + (1.5 X 0.6) = 4.5

So, outlier on High Side.

So,

no outlier

So,

correct option:

No, there are no outliers

Part (i) For 1987:

Part (j)

Slope = - 0.043