Question

The table below shows the life expectancy for an individual born in the United States in certain years. Year of Birth Life Expectancy

CHART W NUMBERS IS BELOW

Part (a) Decide which variable should be the independent variable and which should be the dependent variable.

A)Independent: year of birth; Dependent: life expectancy Independent: life expectancy;

B) Dependent: year of birth Incorrect: Your answer is incorrect.

Part (b) Draw a scatter plot of the ordered pairs.

Part (c) Calculate the least squares line. Put the equation in the form of ŷ = a + bx. (Round your answers to three decimal places.) ŷ = .228 Incorrect: Your answer is incorrect. + -377.283 Incorrect: Your answer is incorrect. x

Part (d) Find the correlation coefficient r. (Round your answer to four decimal places.) r = .9612 Correct:

Is it significant? Yes No

Part (e) Find the estimated life expectancy for an individual born in 1950 and for one born in 2010. (Round your answers to one decimal place.)

Birthdate in 1950:

Birthdate in 2010:

Part (f) Why aren't the answers to part (e) the same as the values in the table that correspond to those years?

A) The answers will be different each time you calculate a least squares line.

B) The answers are different because not all data points will fall on the regression line unless the correlation is perfect.

C) The answers are different because people live longer each year.

D) The answers are different because of errors in recording the life expectancy.

Part (g) Use the two points in part (e) to plot the least squares line on your graph from part (b).

Part (h) Based on the data, is there a linear relationship between the year of birth and life expectancy?

A) Yes, there is a linear relationship between the year of birth and life expectancy.

B) No, there is not a linear relationship between the year of birth and life expectancy.

Part (i) Are there any outliers in the data?

A) Yes, 1930 and 2010 are outliers.

B) Yes, 1930 and 1950 are outliers.

C) Yes, 1950 is an outlier.

D) No, there are no outliers.

Part (j) Using the least squares line, find the estimated life expectancy for an individual born in 1870. (Round your answer to one decimal place.)

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

A) Yes, because the estimate is over 50 years.

B) No, because 1870 is outside the domain of the least squares line.

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

Interpret the slope. (Round your answer to three decimal places.) As the ---Select--- increases by one year, the ---Select--- increases by year
s

year of birth	life expectancy
1930	59.7
1940	62.9
1950	70.2
1965	69.7
1973	71.4
1982	74.5
1987	75
1992	75.7
2010	78.7

Answer 1

"As per the HOMEWORKLIB RULES, we need to answer for the first 4 subparts of the question only in multiple subparts posting. Please repost the other subparts of the question as new question."

Solution:

Part (a) Decide which variable should be the independent variable and which should be the dependent variable.

Here 'year of birth' is independent variable and 'life expectancy' is dependent variable.

Option A is the correct answer.

A)Independent: year of birth; Dependent: life expectancy

Part (b) Draw a scatter plot of the ordered pairs.

The given data is as follows with the scatter plot.

Year of birth(x)	Life expectancy(y)
1930	59.7
1940	62.9
1950	70.2
1965	69.7
1973	71.4
1982	74.5
1987	75
1992	75.7
2010	78.7

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

Let us find the value of slope=b and intercept =a using the following formula.

Year of birth(x)	Life expectancy(y)	x2	y2	xy
1930	59.7	3724900	3564.09	115221
1940	62.9	3763600	3956.41	122026
1950	70.2	3802500	4928.04	136890
1965	69.7	3861225	4858.09	136960.5
1973	71.4	3892729	5097.96	140872.2
1982	74.5	3928324	5550.25	147659
1987	75	3948169	5625	149025
1992	75.7	3968064	5730.49	150794.4
2010	78.7	4040100	6193.69	158187
x=17729	y=637.8	x2=34929611	y2=45504.02	xy=1257635.1

Using the above table let us find the value of ''a' and 'b'.

a=[(637.8*34929611)-(17729*1257635.1)] / [(9*34929611)-17729²]

=-18506792.1 /49058

=-377.243

b=[(9*1257635.10-(17729*637.8)] / [(9*34929611)-17729²]

=11159.7/49058

=0.227

Substituting the values of 'a' and 'b' in the equation ŷ = a + bx.

We have ŷ = -377.243+0.227x

Therefore the least square line is ŷ =0.227x -377.243

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

The correlation coefficient formula is given below:

=[(9*1257635.1)-(17729*637.8)] / [(9*34929611)-17729²] [(9*45504.02)-637.8²]

=11159.7/11609.44

r=0.9613

The correlation coefficient is 0.9613.

Correlation coefficient values less than +0.8 or greater than -0.8 are not considered significant.

Therefore the value of r=0.9613 is greater than +0.8 and hence it is significant.