a) Determine the least-squares regression equation, treating year as the explanatory variable. Choose the correct answer below. OA. ý = 1,236,351x- 3,733,948 в. у- 2,000х -3,733,948 OC. ý = - 3,733,948x + 2,000 O D. ý = 2,000x - 1,499,492 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 a = 0.01 level of significance State the null and alternative hypotheses. Choose the correct answer below. DA. Ho: Po =0 H,: Po #0 Population O B. Ho: B, =0 H: B, #0 Full data set O DC. Ho: P, =0 H,: B, >0 Year, x 1900 1910 1920 1930 1940 1950 Population, y 79,212 95,228 104.021 123,202 132,164 151,325 Year, x 1960 1970 1980 1990 2000 Population, y 179.323 203,302 226,542 248,709 281,421 D D. Ho: Po = 0 Determine the P-value of this hypothesis test. -value = (Round to three decimal places as needed.) Print Done State the appropriate conclusion. Choose the correct answer below. O A. Reject H,: There is not sufficient evidence to conclude that a linear relation exists between year and population. O B. Reject H,. There is sufficient evidence to conclude that a linear relation exists between year and population. O C. Do not reject Ho. There is sufficient evidence to conclude that a linear relation exists between year and population. O D. Do not reject Hn. There is not sufficient evidence to conclude that a linear relation exists between year and population.
a) Determine the least-squares regression equation, treating year as the explanatory variable. Choose the correct answer below. OA. ý = 1,236,351x- 3,733,948 в. у- 2,000х -3,733,948 OC. ý = - 3,733,948x + 2,000 O D. ý = 2,000x - 1,499,492 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 a = 0.01 level of significance State the null and alternative hypotheses. Choose the correct answer below. DA. Ho: Po =0 H,: Po #0 Population O B. Ho: B, =0 H: B, #0 Full data set O DC. Ho: P, =0 H,: B, >0 Year, x 1900 1910 1920 1930 1940 1950 Population, y 79,212 95,228 104.021 123,202 132,164 151,325 Year, x 1960 1970 1980 1990 2000 Population, y 179.323 203,302 226,542 248,709 281,421 D D. Ho: Po = 0 Determine the P-value of this hypothesis test. -value = (Round to three decimal places as needed.) Print Done State the appropriate conclusion. Choose the correct answer below. O A. Reject H,: There is not sufficient evidence to conclude that a linear relation exists between year and population. O B. Reject H,. There is sufficient evidence to conclude that a linear relation exists between year and population. O C. Do not reject Ho. There is sufficient evidence to conclude that a linear relation exists between year and population. O D. Do not reject Hn. There is not sufficient evidence to conclude that a linear relation exists between year and population.
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Concept explainers
Correlation
Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.
Linear Correlation
A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.
Regression Analysis
Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.
Question
Transcribed Image Text: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. Comp
(a) through (f) below.
E 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.
O A. y = 1,236,351x - 3,733,948
O B. ý =2,000x - 3.733.948
OC. y= - 3,733,948x + 2,000
O D. y = 2,000x - 1,499,492
(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 a = 0.01 level of significance
State the null and alternative hypotheses. Choose the correct answer below.
O A. Ho: Po = 0
H;: Bo #0
O Population
— Х
O B. Ho: P, = 0
H,: B, #0
Full data set D
OC. Ho: P, = 0
H,: P, > 0
Year, x
Population, y
79,212
95,228
104,021
123,202
132,164
151,325
Population, y
179,323
203,302
226,542
Year, x
1900
1960
1910
1970
O D. Ho: Po = 0
H;: Po >0
1920
1980
1930
1990
248,709
281,421
1940
1950
2000
Determine the P-value of this hypothesis test.
P-value =O (Round to three decimal places as needed.)
Print
Done
State the appropriate conclusion. Choose the correct answer below.
O A. Reject H,. There is not sufficient evidence to conclude that a linear relation exists between year and population.
O B. Reject Hn. There is sufficient evidence to conclude that a linear relation exists between year and population.
OC. Do not reject Ho. There is sufficient evidence to conclude that a linear relation exists between year and population.
O D. Do not reject Hp. There is not sufficient evidence to conclude that a linear relation exists between year and population.
Transcribed Image Text:(c) Draw a scatter diagram, treating year as the explanatory variable. Choose the correct graph below.
O A.
OB.
OC.
3x 104
3x 10
3x 10
2x102
2x102
2x 102
1x 10
1x 104
1x 10
1900
2000
1900
2000
1900
2000
Year, x
Year, x
Year, x
(d) Plot the residuals against the explanatory variable, year. Choose the correct graph below.
O A.
OB.
OC.
Q
20000-
20000-
20000-
10,000-
10.000•
10,000-
0-
0-
0-
•.
-10,000-
-10,000-
-10,000-•
-20000-
1900
-20000+
1900
2000
-20000-
1900
2000
2000
Year, x
Year, x
Year, x
(e) Does a linear model seem appropriate based on the scatter diagram and residual plot?
O No
O Yes
(f) What is the moral?
O 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.
O 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.
OC. 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.
Population, y
sjenpsa
Population, y
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