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 (a) Using "Year" as the independent variable and "Welfare family size" as the dependent variable, make a scatter plot of the data.

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 (c) Find the correlation coefficient r. (Round your answer to four decimal places.)

r =  

Is it significant?

Yes

No     

Part (d) Find the estimated welfare family size in 1971. (Use your equation from part (b). Round your answer to one decimal place.)

( ) people

Find the estimated welfare family size in 1989. (Use your equation from part (b). Round your answer to one decimal place.)
( ) people

Part (e) Use the two points in part (d) to plot the least squares line.

Part (f) 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     

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

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

The estimate is not accurate because it does not follow the linear trend.

The estimate is not accurate because it is much lower than the observed values in 1983 and 1988.     

The estimate is accurate because it follows the linear trend of the data set and falls within the domain of the data.

The estimate is not accurate because it falls outside the domain.

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

( )

Interpret the slope.

As the Select ( year or size of the welfare family increases by one, the Select ( size of the welfare family oryear, decreases by ( ) .

Answer 1

Part a)

From the scatter, the plot shows that the Welfare family size and the year has a negative association.

b)

The regression equation is
Y = 88.720 - 0.043 X

c)

Pearson correlation of X and Y = -0.853
P-Value = 0.015

Comment: The estimated p-value is 0.015. Hence, we can conclude that the Welfare family size and Year has a significant correlation at 0.05 level of significance.

Is it significant?

Ans: Yes

d)

Part (d) Find the estimated welfare family size in 1971. (Use your equation from part (b). Round your answer to one decimal place.)

Ans: The estimated welfare family size in 1971 is

Y = 88.720 - 0.043 *1971 =3.967 =4.0 people.

Find the estimated welfare family size in 1989. (Use your equation from part (b). Round your answer to one decimal place.)

The estimated welfare family size in 1989 is

Y = 88.720 - 0.043 *1989= 3.2 people.

Part (e) The two points in part (d) to plot the least squares line are (1971, 4.0) and (1989, 3.2).

Part (f) Based on the above data, is there a linear relationship between the year and the average number of people in a welfare family?

Ans: Yes. Because of the significant correlation coefficient at 0.05 level of significance.