Question

Is the number of tornadoes increasing? In the last homework, data on the number of tornadoes in the United States between 1953 and 2014 were analyzed to see if there was a linear trend over time. Some argue that it’s not the number of tornadoes increasing over time, but rather the probability of sighting them because there are more people living in the United States. Let’s investigate this by including the U.S. census count (in thousands) as an additional explanatory variable (data in EX11-24TWISTER.csv).

Perform a multiple regression using both year and census count as explanatory variables. Write down the fitted model. Are year and census count respectively significant in the MLR model?

Year	Tornadoes	Census
1953	421	158956
1954	550	161884
1955	593	165069
1956	504	168088
1957	856	171187
1958	564	174149
1959	604	177135
1960	616	179979
1961	697	182992
1962	657	185771
1963	464	188483
1964	704	191141
1965	906	193526
1966	585	195576
1967	926	197457
1968	660	199399
1969	608	201385
1970	653	203984
1971	888	206827
1972	741	209284
1973	1102	211357
1974	947	213342
1975	920	215465
1976	835	217563
1977	852	219760
1978	788	222095
1979	852	224567
1980	866	227225
1981	783	229466
1982	1046	231664
1983	931	233792
1984	907	235825
1985	684	237924
1986	764	240133
1987	656	242289
1988	702	244499
1989	856	246819
1990	1133	249623
1991	1132	252981
1992	1298	256514
1993	1176	259919
1994	1082	263126
1995	1235	266278
1996	1173	269394
1997	1148	272647
1998	1449	275854
1999	1340	279040
2000	1075	282224
2001	1215	285318
2002	934	288369
2003	1374	290447
2004	1817	293191
2005	1265	295895
2006	1103	298754
2007	1096	301621
2008	1692	304059
2009	1156	308746
2010	1282	309347
2011	1691	311722
2012	938	314112
2013	907	316498
2014	888	318857

Answer 1

The multiple regression equation is of the form,

where

​ is the dependent variable "Number of tornadoes".

is the independent variable "Year"

​ is the independent variable "Census"

is the intercept

is the slope coefficient of variable "Year"

​ is the slope coefficient of variable "Census"

​ is the error term

R OUTPUT OF MULTIPLE LINEAR REGRESSION MODEL:

From the output, the equation for fitted model is given by,

is the predicted dependent variable "Number of tornadoes".

is the independent variable "Year"

​ is the independent variable "Census"

Intercept is ​. That is mean number of tornadoes without involving the independent variables year and census is 2.

The slope coefficient of variable "Year" is ​. That is, as the year increases by 1, the mean number of tornadoes decreases by 10.

The slope coefficient of variable "Census" ​ is ​. That is, as the census count increases by 1000, the mean number of tornadoes increases by 0.009.

But the variables Year and Census are not significant variables, since the p values for year (0.706) and census (0.378) are greater than the significance level ​, we fail to reject null hypothesis and conclude that the variables year and census are not significant variables.

And we could see that adjusted R-square value is ​. Thus only 56% of the total variation in dependent variable is explained by the independent variables year and census. Thus these two variables year and census are not significant enough in explaining the dependent variable "number of tornadoes".