Question

The data in the accompanying table represent the population of a certain country every 10 years for the years​ 1900-2000. An ecologist is interested in finding an equation that describes the population of the country over time. Complete parts ​(a) through ​(f) below. LOADING... Click the icon to view the data table. ​(a) Determine the​ least-squares regression​ equation, treating year as the explanatory variable. Choose the correct answer below. A. ModifyingAbove y with caretequals2 comma 022xnegative 1 comma 542 comma 401 B. ModifyingAbove y with caretequalsnegative 3 comma 776 comma 857xplus2 comma 022 C. ModifyingAbove y with caretequals2 comma 022xnegative 3 comma 776 comma 857 D. ModifyingAbove y with caretequals1 comma 236 comma 373xnegative 3 comma 776 comma 857 ​(b) A normal probability plot of the residuals indicates that the residuals are approximately normally distributed. Test whether a linear relation exists between year and population. Use the alphaequals0.01 level of significance. State the null and alternative hypotheses. Choose the correct answer below. A. Upper H 0​: beta 1 equals 0 Upper H 1​: beta 1 not equals 0 B. Upper H 0​: beta 1 equals 0 Upper H 1​: beta 1 greater than 0 C. Upper H 0​: beta 0 equals 0 Upper H 1​: beta 0 greater than 0 D. Upper H 0​: beta 0 equals 0 Upper H 1​: beta 0 not equals 0 Determine the​ P-value of this hypothesis test. ​P-valueequals nothing ​(Round to three decimal places as​ needed.) State the appropriate conclusion. Choose the correct answer below. A. Reject Upper H 0. There is sufficient evidence to conclude that a linear relation exists between year and population. B. Reject Upper H 0. There is not sufficient evidence to conclude that a linear relation exists between year and population. C. Do not reject Upper H 0. There is sufficient evidence to conclude that a linear relation exists between year and population. D. Do not reject Upper H 0. There is not sufficient evidence to conclude that a linear relation exists between year and population. ​(c) Draw a scatter​ diagram, treating year as the explanatory variable. Choose the correct graph below. A. 1900 2000 Year, x Population, y font size decreased by 3 1 times 10 Superscript 5 font size decreased by 3 2 times 10 Superscript 5 font size decreased by 3 3 times 10 Superscript 5 A scatter diagram has a horizontal axis labeled Year, x from 1900 to 2000 in increments of 100 and a vertical axis labeled Population, y from 0 to 4 times 10 Superscript 5 in increments of 1 times 10 Superscript 5. A series of plotted points closely follow the pattern of a line rising from left to right passing through the points (1900, 80000) and (2000, 280000). All coordinates are approximate. B. 1900 2000 Year, x Population, y font size decreased by 3 1 times 10 Superscript 5 font size decreased by 3 2 times 10 Superscript 5 font size decreased by 3 3 times 10 Superscript 5 A scatter diagram has a horizontal axis labeled Year, x from 1900 to 2000 in increments of 100 and a vertical axis labeled Population, y from 0 to 4 times 10 Superscript 5 in increments of 1 times 10 Superscript 5. From left to right, a series of plotted points closely follow the pattern of a line rising passing through the point (1900, 80000) to the point (1950, 150000), and then closely follow the pattern of a line falling to the point (2000, 80000). All coordinates are approximate. C. 1900 2000 Year, x Population, y font size decreased by 3 1 times 10 Superscript 5 font size decreased by 3 2 times 10 Superscript 5 font size decreased by 3 3 times 10 Superscript 5 A scatter diagram has a horizontal axis labeled Year, x from 1900 to 2000 in increments of 100 and a vertical axis labeled Population, y from 0 to 4 times 10 Superscript 5 in increments of 1 times 10 Superscript 5. A series of plotted points closely follow the pattern of a line falling from left to right passing through the points (1900, 280000) and (2000, 80000). All coordinates are approximate. ​(d) Plot the residuals against the explanatory​ variable, year. Choose the correct graph below. A. 1900 2000 0 -10,000 10,000 -20000 20000 Year, x Residuals A scatter diagram has a horizontal axis labeled Year, x from 1900 to 2000 in increments of 100 and a vertical axis labeled Residuals from negative 20,000 to 20,000 in increments of 10,000. From left to right, a series of plotted points follow the pattern of a curve rising passing through the point (1900, negative 8000) to a maximum at the point (1920, negative 1000), falling to a minimum at the point (1950, negative 15000), rising to a maximum at the point (1980, 0), and falling to the point (2000, negative 14000). All coordinates are approximate. B. 1900 2000 0 -10,000 10,000 -20000 20000 Year, x Residuals A scatter diagram has a horizontal axis labeled Year, x from 1900 to 2000 in increments of 100 and a vertical axis labeled Residuals from negative 20,000 to 20,000 in increments of 10,000. A series of plotted points closely follow the pattern of a line rising from left to right passing through the points (1900, negative 13000) and (2000, 5000). All coordinates are approximate. C. 1900 2000 0 -10,000 10,000 -20000 20000 Year, x Residuals A scatter diagram has a horizontal axis labeled Year, x from 1900 to 2000 in increments of 100 and a vertical axis labeled Residuals from negative 20,000 to 20,000 in increments of 10,000. From left to right, a series of plotted points follow the pattern of a curve falling passing through the point (1900, 8000) to a minimum at the point (1950, negative 15000), and then rising at a decreasing rate passing through the point (1990, 2000). A point is plotted at (2000, 14000). All coordinates are approximate. ​(e) Does a linear model seem appropriate based on the scatter diagram and residual​ plot? Yes No ​(f) What is the​ moral? A. The moral is that explanatory variables may indicate that a linear relation between the two variables does not exist even though diagnostic tools​ (such as residual​ plots) indicate that a linear model is appropriate. B. The moral is that inferential procedures may indicate that a linear relation between the two variables exists even though diagnostic tools​ (such as residual​ plots) indicate that a linear model is inappropriate. C. The moral is that inferential procedures may indicate that a nonlinear relation between the two variables exists even though diagnostic tools​ (such as residual​ plots) indicate that a linear model is appropriate. Click to select your answer(s).

Year, x   Population, y
1900   73212
1910   95228
1920   106021
1930   123202
1940   132164
1950   151325
1960   179323
1970   203302
1980   226542
1990   248709
2000   281421

Answer 1

All options are very confusing.

Hence I am going to give exact answer

You should match them

data

x	y
1900	73212
1910	95228
1920	106021
1930	123202
1940	132164
1950	151325
1960	179323
1970	203302
1980	226542
1990	248709
2000	281421

regression

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.990775529
R Square	0.98163615
Adjusted R Square	0.979595722
Standard Error	9667.240032
Observations	11
ANOVA
	df	SS	MS	F	Significance F
Regression	1	44960828908	44960828908	481.0932963	4.01703E-09
Residual	9	841099768.5	93455529.84
Total	10	45801928677
	Coefficients	Standard Error	t Stat	P-value	Lower 95%
Intercept	-3776856.864	179761.9911	-21.01031949	5.87643E-09	-4183506.739
x	2021.719091	92.17351712	21.93383907	4.01703E-09	1813.208109

y^= -3776857 + 2022 x

b)

TS = 21.93338

p-value = 0.0000

we reject the null hypothesie

there is sufficient evidence to conclude that there is linear relationship

c)

scatterplot

d)

RESIDUAL PLOT

e)

No

linear model is not appropriate

f)

B. The moral is that inferential procedures may indicate that a linear relation between the two variables exists even though diagnostic tools​ (such as residual​ plots) indicate that a linear model is inappropriate.