Question

In: Statistics and Probability

Use the data and Excel to answer this question. It contains the United States Census Bureau’s...

Use the data and Excel to answer this question. It contains the United States Census Bureau’s estimates for World Population from 1950 to 2014. You will find a column of dates and a column of data on the World Population for these years. Generate the time variable t. Then run a regression with the Population data as a dependent variable and time as the dependent variable. Have Excel report the residuals.

(a) Based on the ANOVA table and t-statistics, does the regression appear significant?

(b) Calculate the Durbin-Watson Test statistic. Is there a serial correlation problem with the data? Explain.

(d) What affect might your answer in part (b) have on your conclusions in part (a)?

Year Population
1950 2,557,628,654
1951 2,594,939,877
1952 2,636,772,306
1953 2,682,053,389
1954 2,730,228,104
1955 2,782,098,943
1956 2,835,299,673
1957 2,891,349,717
1958 2,948,137,248
1959 3,000,716,593
1960 3,043,001,508
1961 3,083,966,929
1962 3,140,093,217
1963 3,209,827,882
1964 3,281,201,306
1965 3,350,425,793
1966 3,420,677,923
1967 3,490,333,715
1968 3,562,313,822
1969 3,637,159,050
1970 3,712,697,742
1971 3,790,326,948
1972 3,866,568,653
1973 3,942,096,442
1974 4,016,608,813
1975 4,089,083,233
1976 4,160,185,010
1977 4,232,084,578
1978 4,304,105,753
1979 4,379,013,942
1980 4,451,362,735
1981 4,534,410,125
1982 4,614,566,561
1983 4,695,736,743
1984 4,774,569,391
1985 4,856,462,699
1986 4,940,571,232
1987 5,027,200,492
1988 5,114,557,167
1989 5,201,440,110
1990 5,288,955,934
1991 5,371,585,922
1992 5,456,136,278
1993 5,538,268,316
1994 5,618,682,132
1995 5,699,202,985
1996 5,779,440,593
1997 5,857,972,543
1998 5,935,213,248
1999 6,012,074,922
2000 6,088,571,383
2001 6,165,219,247
2002 6,242,016,348
2003 6,318,590,956
2004 6,395,699,509
2005 6,473,044,732
2006 6,551,263,534
2007 6,629,913,759
2008 6,709,049,780
2009 6,788,214,394
2010 6,858,584,755
2011 6,935,999,491
2012 7,013,871,313
2013 7,092,128,094
2014 7,169,968,185

Can you please give detailed steps to do on excel?

Solutions

Expert Solution

(a) (4 marks) Based on the ANOVA table and t-statistics, does the regression appear significant?

The p-value is 0.0000.

Since the p-value (0.0000) is less than the significance level (0.05), we can reject the null hypothesis.

Therefore, we can conclude that the regression appears significant.

(b) (10 marks) Calculate the Durbin-Watson Test statistic. Is there a serial correlation problem with the data? Explain.

The Durbin-Watson Test statistic is 0.02. Yes, serial correlation is a problem with the data as the test statistic is very low.

(d) (4 marks) What affect might your answer in part (b) have on your conclusions in part (a)?

The autocorrelation of the variables will result in incorrect conclusions.

r² 0.997
r   0.998
Std. Error   83962741.129
n   65
k   1
Dep. Var. Population
ANOVA table
Source SS   df   MS F p-value
Regression 12,90,79,66,35,65,23,10,00,000.0000 1   12,90,79,66,35,65,23,10,00,000.0000 18309.84 2.29E-79
Residual 4,44,13,37,39,56,39,33,000.0000 63   7,04,97,41,89,78,40,210.0000
Total 12,95,23,79,73,04,79,50,00,000.0000 64  
Regression output confidence interval
variables coefficients std. error    t (df=63) p-value 95% lower 95% upper
Intercept 2,22,24,52,729.0091
Year 7,51,10,543.1167 5,55,083.8585 135.314 2.29E-79 7,40,01,296.5378 7,62,19,789.6956
Observation Population Predicted Residual
1 2,55,76,28,654.0 2,29,75,63,272.1 26,00,65,381.9
2 2,59,49,39,877.0 2,37,26,73,815.2 22,22,66,061.8
3 2,63,67,72,306.0 2,44,77,84,358.4 18,89,87,947.6
4 2,68,20,53,389.0 2,52,28,94,901.5 15,91,58,487.5
5 2,73,02,28,104.0 2,59,80,05,444.6 13,22,22,659.4
6 2,78,20,98,943.0 2,67,31,15,987.7 10,89,82,955.3
7 2,83,52,99,673.0 2,74,82,26,530.8 8,70,73,142.2
8 2,89,13,49,717.0 2,82,33,37,073.9 6,80,12,643.1
9 2,94,81,37,248.0 2,89,84,47,617.1 4,96,89,630.9
10 3,00,07,16,593.0 2,97,35,58,160.2 2,71,58,432.8
11 3,04,30,01,508.0 3,04,86,68,703.3 -56,67,195.3
12 3,08,39,66,929.0 3,12,37,79,246.4 -3,98,12,317.4
13 3,14,00,93,217.0 3,19,88,89,789.5 -5,87,96,572.5
14 3,20,98,27,882.0 3,27,40,00,332.6 -6,41,72,450.6
15 3,28,12,01,306.0 3,34,91,10,875.8 -6,79,09,569.8
16 3,35,04,25,793.0 3,42,42,21,418.9 -7,37,95,625.9
17 3,42,06,77,923.0 3,49,93,31,962.0 -7,86,54,039.0
18 3,49,03,33,715.0 3,57,44,42,505.1 -8,41,08,790.1
19 3,56,23,13,822.0 3,64,95,53,048.2 -8,72,39,226.2
20 3,63,71,59,050.0 3,72,46,63,591.3 -8,75,04,541.3
21 3,71,26,97,742.0 3,79,97,74,134.5 -8,70,76,392.5
22 3,79,03,26,948.0 3,87,48,84,677.6 -8,45,57,729.6
23 3,86,65,68,653.0 3,94,99,95,220.7 -8,34,26,567.7
24 3,94,20,96,442.0 4,02,51,05,763.8 -8,30,09,321.8
25 4,01,66,08,813.0 4,10,02,16,306.9 -8,36,07,493.9
26 4,08,90,83,233.0 4,17,53,26,850.0 -8,62,43,617.0
27 4,16,01,85,010.0 4,25,04,37,393.2 -9,02,52,383.2
28 4,23,20,84,578.0 4,32,55,47,936.3 -9,34,63,358.3
29 4,30,41,05,753.0 4,40,06,58,479.4 -9,65,52,726.4
30 4,37,90,13,942.0 4,47,57,69,022.5 -9,67,55,080.5
31 4,45,13,62,735.0 4,55,08,79,565.6 -9,95,16,830.6
32 4,53,44,10,125.0 4,62,59,90,108.7 -9,15,79,983.7
33 4,61,45,66,561.0 4,70,11,00,651.9 -8,65,34,090.9
34 4,69,57,36,743.0 4,77,62,11,195.0 -8,04,74,452.0
35 4,77,45,69,391.0 4,85,13,21,738.1 -7,67,52,347.1
36 4,85,64,62,699.0 4,92,64,32,281.2 -6,99,69,582.2
37 4,94,05,71,232.0 5,00,15,42,824.3 -6,09,71,592.3
38 5,02,72,00,492.0 5,07,66,53,367.4 -4,94,52,875.4
39 5,11,45,57,167.0 5,15,17,63,910.6 -3,72,06,743.6
40 5,20,14,40,110.0 5,22,68,74,453.7 -2,54,34,343.7
41 5,28,89,55,934.0 5,30,19,84,996.8 -1,30,29,062.8
42 5,37,15,85,922.0 5,37,70,95,539.9 -55,09,617.9
43 5,45,61,36,278.0 5,45,22,06,083.0 39,30,195.0
44 5,53,82,68,316.0 5,52,73,16,626.1 1,09,51,689.9
45 5,61,86,82,132.0 5,60,24,27,169.3 1,62,54,962.7
46 5,69,92,02,985.0 5,67,75,37,712.4 2,16,65,272.6
47 5,77,94,40,593.0 5,75,26,48,255.5 2,67,92,337.5
48 5,85,79,72,543.0 5,82,77,58,798.6 3,02,13,744.4
49 5,93,52,13,248.0 5,90,28,69,341.7 3,23,43,906.3
50 6,01,20,74,922.0 5,97,79,79,884.8 3,40,95,037.2
51 6,08,85,71,383.0 6,05,30,90,428.0 3,54,80,955.0
52 6,16,52,19,247.0 6,12,82,00,971.1 3,70,18,275.9
53 6,24,20,16,348.0 6,20,33,11,514.2 3,87,04,833.8
54 6,31,85,90,956.0 6,27,84,22,057.3 4,01,68,898.7
55 6,39,56,99,509.0 6,35,35,32,600.4 4,21,66,908.6
56 6,47,30,44,732.0 6,42,86,43,143.5 4,44,01,588.5
57 6,55,12,63,534.0 6,50,37,53,686.7 4,75,09,847.3
58 6,62,99,13,759.0 6,57,88,64,229.8 5,10,49,529.2
59 6,70,90,49,780.0 6,65,39,74,772.9 5,50,75,007.1
60 6,78,82,14,394.0 6,72,90,85,316.0 5,91,29,078.0
61 6,85,85,84,755.0 6,80,41,95,859.1 5,43,88,895.9
62 6,93,59,99,491.0 6,87,93,06,402.2 5,66,93,088.8
63 7,01,38,71,313.0 6,95,44,16,945.4 5,94,54,367.6
64 7,09,21,28,094.0 7,02,95,27,488.5 6,26,00,605.5
65 7,16,99,68,185.0 7,10,46,38,031.6 6,53,30,153.4
Durbin-Watson = 0.02

NOTE:: I HOPE YOUR HAPPY WITH MY ANSWER.......***PLEASE SUPPORT ME WITH YOUR RATING.....

***PLEASE GIVE ME "LIKE".....THANK YOU

orchestra answered 1 year ago
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