Question

Question 2 Situation: A think tank wants to examine recent assertions about whether lobster consumption and number of college enrollments predict coastal Western Hemisphere countries’ total GDP. Annual data were collected for the last 40 years. Lobster consumption was measured in 10,000,000 pound units of lobster. Number of college enrollments was measured in 10,000,000 individuals units enrolled in at least one college or university course per the fall and spring semesters for a minimum of two courses per year. GDP was measured in nominal percentage growth. First, run descriptive statistics. Next, run a multiple linear regression where lobster consumption and college enrollments are the predictors (independent variables) and GDP is the dependent variable. Alpha = .05. Are the data normally distributed? Do lobster consumption and college enrollments predict GDP? Report and interpret (explain) your results including the skewness and kurtosis statistics for each variable, overall regression p-value, r-square, predictor coefficients and their p-values, and sample size. Be sure to explain the overall contribution of the model in explaining change in the dependent variable as well as the individual predictor contribution to change in the dependent variable. Based on your results, would you make any recommendations about additional analysis (65% of assignment points).

GDP	Lobster	Enrollments	Lobster (00,000,000)	Enrollments (00,000,000)
1.18	300,000,000	13,761,737	30.0000	1.3762
2.28	168,005,852	35,000,000	16.8006	3.5000
2.37	300,000,000	42,000,000	30.0000	4.2000
2.37	171,886,564	38,811,068	17.1887	3.8811
5.85	300,000,000	56,016,072	30.0000	5.6016
-0.57	100,000,000	10,000,000	10.0000	1.0000
4.47	300,000,000	55,216,617	30.0000	5.5217
1.24	75,000,000	30,000,000	7.5000	3.0000
2.97	235,304,976	45,000,000	23.5305	4.5000
2.36	202,998,799	25,000,000	20.2999	2.5000
2.99	231,600,131	30,000,000	23.1600	3.0000
2.44	173,174,519	23,297,388	17.3175	2.3297
0.72	150,000,000	14,691,020	15.0000	1.4691
0.56	100,000,000	32,000,000	10.0000	3.2000
3.05	263,823,576	41,360,064	26.3824	4.1360
2.36	150,378,241	40,000,000	15.0378	4.0000
3.12	270,730,403	42,440,763	27.0730	4.2441
-1.79	120,000,000	20,000,000	12.0000	2.0000
3.82	400,000,000	31,755,949	40.0000	3.1756
7.69	300,000,000	30,000,000	30.0000	3.0000
5.12	395,000,000	26,320,490	39.5000	2.6320
6.52	300,000,000	60,618,467	30.0000	6.0618
2.78	188,647,991	33,778,258	18.8648	3.3778
-1.25	50,000,000	20,000,000	5.0000	2.0000
3.92	357,750,427	55,948,661	35.7750	5.5949
4.74	395,000,000	42,279,580	39.5000	4.2280
-0.98	35,000,000	45,000,000	3.5000	4.5000
1.34	70,522,208	9,807,424	7.0522	0.9807
2.05	131,319,757	11,892,034	13.1320	1.1892
3.75	295,721,911	7,649,064	29.5722	0.7649
3.76	303,489,724	64,061,968	30.3490	6.4062
4.48	385,919,736	76,124,744	38.5920	7.6125
0.93	38,703,734	12,044,349	3.8704	1.2044
0.47	20,000,000	32,000,000	2.0000	3.2000
0.44	78,000,000	9,257,624	7.8000	0.9258
0.99	45,082,034	11,725,510	4.5082	1.1726
1.88	123,452,084	47,975,552	12.3452	4.7976
3.04	210,343,787	44,833,849	21.0344	4.4834
2.53	177,362,455	40,000,000	17.7362	4.0000
4.58	325,000,000	11,238,401	32.5000	1.1238

Answer 1

Descriptive Statistics using Real statistics Add-In in EXCEL

Descriptive Statistics
Descriptive Statistics GDP Lobster Enrollments Mean 2.51425 205980472.7 32972666.33 Standard Error 0.326381853 18001675.63 2728395.891 Median 2.405 195823395 32000000 Mode 2.37 300000000 30000000 Standard Deviation 2.064220083 113852593.4 17255890.75 Sample Variance 4.261004551 1.29624E+16 2.97766E+14 Kurtosis 0.203045278 -1.143494722 -0.42315343 Skewness 0.161005249 0.065115169 0.354205687 Range 9.48 380000000 68475680 Maximum 7.69 400000000 76124744 Minimum -1.79 20000000 7649064 Sum 100.57 8239218909 1318906653 Count 40 40 40 Geometric Mean #NUM! 165489043.2 27960557.73 Harmonic Mean #NUM! 117230463.7 22810802.02 AAD 1.5704625 97802784.46 13999250.14 MAD 1.385 104176605 12416924.5 IQR 2.6425 185000000 24366279.5

Using EXCEL DATA > DATA analysis > regression

Input Y: GDF

Input X: Lobsters, enrollments

Ok

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.807229605
R Square	0.651619635
Adjusted R Square	0.632788264
Standard Error	1.250876045
Observations	40
ANOVA
	df	SS	MS	F	Significance F
Regression	2	108.2856149	54.14280747	34.6028779	3.37282E-09
Residual	37	57.89356255	1.56469088
Total	39	166.1791775
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	-0.778810642	0.479926025	-1.622772263	0.113129217	-1.751233137	0.193611853
Lobster	1.33051E-08	1.97528E-09	6.735792059	6.39218E-08	9.30279E-09	1.73074E-08
Enrollments	1.67554E-08	1.30327E-08	1.28564316	0.206556211	-9.65137E-09	4.31622E-08

Are the data normally distributed? Do lobster consumption and college enrollments predict GDP? Report and interpret (explain) your results including the skewness and kurtosis statistics for each variable, overall regression p-value, r-square, predictor coefficients and their p-values, and sample size.

Shapiro-Wilk Test
	GDP	Lobster	Enrollments
W-stat	0.987659	0.947955336	0.956847113
p-value	0.93455	0.064502867	0.130556972
alpha	0.05	0.05	0.05
normal	yes	yes	yes

Box Plot
	GDP	Lobster	Enrollments
Min	0	20000001.79	7649065.79
Q1-Min	2.9225	95000000	11023691
Med-Q1	1.2725	80823395	13327245
Q3-Med	1.37	104176605	11039034.5
Max-Q3	3.915	100000000	33085709.5
Mean	4.30425	205980474.5	32972668.12
Min	-1.79	20000000	7649064
Q1	1.1325	115000000	18672755
Median	2.405	195823395	32000000
Q3	3.775	300000000	43039034.5
Max	7.69	400000000	76124744
Mean	2.51425	205980472.7	32972666.33

Using Shapiro Wilks test to test for normality of the data. The null hypothesis for this test is that the data are normally distributed. If the chosen alpha level is 0.05 and the p-value is less than 0.05, then the null hypothesis that the data are normally distributed is rejected. If the p-value is greater than 0.05, then the null hypothesis is not rejected.

Since our all three data variables have the p-value is greater than 0.05, then the null hypothesis is not rejected. Thus we can conclude that our data us normal

The linear regression model is given by

The ANOVA of the regression gives F(2,37) = 34.60, p =3.372E-09. Thus it is significant. The coefficient of determination r-square is 0.6516 which implies 65.16% of the variation in GDP is explained by lobster consumption and college enrollments. Though the p-value of the coefficient is not significant as it more than 0.05.