Question

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

(b) (10 marks) Calculate the Durbin-Watson Test statistic. Is there a serial correlation problem with the data? Explain. (d) (4 marks) 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

Answer 1

a)

The regression equation is defined as,

Where the dependent variable Y = Population and independent variable t = year

Now, the regression analysis is done in excel by following steps

Step 1: Write the data values in excel. The screenshot is shown below,

(assign the t = 0 for year 1950)

Step 2: DATA > Data Analysis > Regression > OK. The screenshot is shown below,

Step 3: Select Input Y Range: 'Hours' column, Input X Range: 'Feet and Large' column then OK. The screenshot is shown below, (Click on Residual and Residual plot for residual analysis)

The result is obtained. The screenshot is shown below,

Conclusion:

Overall Significance

From the regression output summary (ANOVA table)

	Significance F
Regression	2.28529E-79

The significance F value is 2.28529E-79 which is greater than 0.05 at a 5% significance level which means the model fits the data value at the 5% significance level. Hence we can conclude that the independent variable year fits the model significantly.

Significance of Independent variable

From the regression output summary (t table)

	P-value
Year	2.28529E-79

The P-value for the independent variable is less than 0.05 at a 5% significance level hence we can conclude that independent variable is not significant in the model.

b)

The Durbin Watson test statistic is obtained using the formula,

Where N = 64, Yi is the current year's observation value and Yi-1 is the previous year's observation value.

From the data values,

From the data values,

The Durwin Watson statistic between 0 to 2 shows positive autocorrelation.

Consequences of positive autocorrelation (serial correlation)

The estimate of the standard error of estimate in the regression analysis is wrong, such that the model underestimates (less than) the true value of the standard error of the estimate.