Question

Question 3 is the same as 10.19 below, they are just for reference.

Please do question 4.

please use R to do this question, provide R codes.

Questlon 3 (6 polnts total) The Storm Prediction Center of the National Ocesnic and Atmospheric Administration maintains a database of tornadoes, floods, and other weather phenomena. The fle "EX10-19TWISTER.CaV Includes the anmual mumber of tornadoes in the Untted States between 1953 and 2014. Use R to carry out the analysts and answer the following: a) (2 potnts) Makea plot of the total mumber of tornadoes by year. Dos a linear trend over years appear reasonable? Are there any outlers or unusual paterns? Explain your answer. b) (2 potnts) Run the stmple linear regression and report the least-squares regresston line. c) (1 potnt) A friend of yours thinks you made a mistake fitting the model because b ts a large negative value. Explain to him why this is not a mistake. d) (1 potnt) Obtain the residuals and plot them versus year. Are there any unusual patterns or cas you did not discuss in part a? If so, comment on them. es that Question 4 (5 points total) Refer to the previous exerctse. Let's proceed with Inference. a) (1 point) Do these data support a linear trend in the number of tornadoes? Justify your answer. b) (2 potnts) Construct a 95% confldence interval for the average number of tornadoes. Explatn how this interval can be used to justify your response In part a. c) (1 point) What Is the predicted number of tornadoes in 2015? d) (1 potnt) Provide an Interval that should contatn the actual count of tornadoes In 2013, 95% of the time. 10.19 Or ot ol Which variable do you think is the best single aplanatory variable of average debt? Explain your answer a18 Are the two fuel efficiency measurements similar? Refer to Exercise 7.32 (page 429), In addition to he computer calculating miles per gallon (mpg), the ver also measured mpg by dividing the miles driven by he mumber of gallons at fill-up. The driver wants to determine if these calculations are similar. MPGDIFF 10.19 Is the number of tornadoes increasing? The Storm Prediction Center of the National Oceanic and Atmospheric Administration maintains a database of tornadoes, floods, and other weather phenomena Table 10.1 summarizes the annual mumber of tornadoes in the United States between 1953 and 2014 TWISTER (a) Make a lot of the total number of tornadoes by year Does a linear trend over years appear reasonable? Are there any outliers or unusual patterns? Explain vour answer (b) Run the simple linear regression and report the least- squares regression line 2 3 4 1 7 Computer 41.5 50.7 36.6 37.3 342 45.0 48.0 43.2 47.7 42.2 36.5 44.2 37.2 35.6 30.5 40,5 40.0 41 0 428 39.2 9 10 (c) A friend of yours thinks you made a mistake fitting the model because bo is a him why this is not a mistake. aiver large negative value. Explain 12 13 14 11 15 16 17 18 il-p 19 20 Computer 43.2 44.6 48.4 46.4 46.8 39.2 37.3 43 5 44.3 43.3 18 8 44 5 45.4 45.3 45.7 34.2 35.2 39 8 44.9 475 (d) Obtain the residuals and plot them versus year. Are there any unusual patterns or cases that you did not discuss in part (a)? If so, comment on them. Driver TABLE 10.1 Annual Number of Tornadoes in The United States Between 1953 and 2014 Number of Number of Number of Number of tornadoes Year tornadoes Year tornadoes Year tornadoes Year 1953 421 1969 608 1985 684 2001 1215 1954 550 1970 653 1986 764 2002 934 593 1971 1955 888 1987 656 2003 1374 1956 504 1972 741 1988 702 2004 1817 1973 1102 1989 856 2005 1265 1957 856 947 1990 1133 2006 1103 1974 1958 564 2007 1096 1991 1132 920 1975 1959 604 2008 1298 1692 1992 835 1976 1960 616 2009 1156 1993 1176 852 1977 1961 697 2010 1282 1082 1994 788 1978 657 1962 2011 1235 1691 1995 852 1979 1963 464 938 2012 1173 1996 866 1980 704 1964 2013 907 1148 1997 783 1981 906 1965 2014 888 1449 1998 1046 1982 585 1966 1340 1999 931 1983 926 1967 1075 2000 907 1984 1968 660

Answer 1

(a)

R-code:

attach(tornadoesinUS)

plot(wt, mpg, main="Scatterplot Example",

xlab="Year ", ylab="Number of tornadoes ", pch=62)

Following is the scatter plot of the data:

2000 1800 1600 1400 1200 1000 800 600 400 200 0 1940 1950 1960 1970 1980 1990 2000 2010 2020 Year Number of tornadoes

Scatter plot shows that there is a strong linear and positive relationship between the variables. There is no outliers.

(b)

Independent variable, X: year

Dependent variable, Y: number of tornadoes

Following is the output of linear regression:

Regression Analysis r2 0.574 62 k 1 0.758 Std. Error 201.406 Dep. Var. Number of tornadoes ANOVA table Source SS df MS p-value 1.03E-12 32,77,236.1910 40,564.3691 Regression 32,77,236.1910 Residual 24,33,862.1477 Total 57,11,098.3387 1 80.79 60 61 Regression output confidence interval 95% upper t (df 60) std. error p-value 95% lower variables coefficients Intercept -24,542.4387 2,835.1878 -8.656 3.75E-12 -30,213.6586 -18,871.2188 15.7064 Year 12.8473 1.4293 8.988 1.03E-12 9.9883

The regression line is:

y' = -24542.4387 + 12.8473* x

(c)

It is not mistake. Intercept is large because value of independent variable year is large.

(d)

R-code:

> plot(torndoseinUS, eruption.res,
+     ylab="Residuals", xlab="year",
+     main="torndoesinUS")
> abline(0, 0)

Following is the residual plot:

Residuals by Year 805.6 604.2 402.8 201.4 0.0 -201.4 -402.8 -604.2 1,940 1,950 1,960 1,970 1,980 1,990 2,000 2,010 2,020 Year Residual (gridl ines std. error)

It shows a random pattern. That is we can assume that condition for regression has been full-filled and it is a good fit.

Residual table;

Observation	Number of tornadoes	Predicted	Residual
1	421.0	548.4	-127.4
2	550.0	561.3	-11.3
3	593.0	574.1	18.9
4	504.0	587.0	-83.0
5	856.0	599.8	256.2
6	564.0	612.7	-48.7
7	604.0	625.5	-21.5
8	616.0	638.4	-22.4
9	697.0	651.2	45.8
10	657.0	664.1	-7.1
11	464.0	676.9	-212.9
12	704.0	689.8	14.2
13	906.0	702.6	203.4
14	585.0	715.4	-130.4
15	926.0	728.3	197.7
16	660.0	741.1	-81.1
17	608.0	754.0	-146.0
18	653.0	766.8	-113.8
19	888.0	779.7	108.3
20	741.0	792.5	-51.5
21	1,102.0	805.4	296.6
22	947.0	818.2	128.8
23	920.0	831.1	88.9
24	835.0	843.9	-8.9
25	852.0	856.8	-4.8
26	788.0	869.6	-81.6
27	852.0	882.5	-30.5
28	866.0	895.3	-29.3
29	783.0	908.2	-125.2
30	1,046.0	921.0	125.0
31	931.0	933.9	-2.9
32	907.0	946.7	-39.7
33	684.0	959.5	-275.5
34	764.0	972.4	-208.4
35	656.0	985.2	-329.2
36	702.0	998.1	-296.1
37	856.0	1,010.9	-154.9
38	1,133.0	1,023.8	109.2
39	1,132.0	1,036.6	95.4
40	1,298.0	1,049.5	248.5
41	1,176.0	1,062.3	113.7
42	1,082.0	1,075.2	6.8
43	1,235.0	1,088.0	147.0
44	1,173.0	1,100.9	72.1
45	1,148.0	1,113.7	34.3
46	1,449.0	1,126.6	322.4
47	1,340.0	1,139.4	200.6
48	1,075.0	1,152.3	-77.3
49	1,215.0	1,165.1	49.9
50	934.0	1,178.0	-244.0
51	1,374.0	1,190.8	183.2
52	1,817.0	1,203.6	613.4
53	1,265.0	1,216.5	48.5
54	1,103.0	1,229.3	-126.3
55	1,096.0	1,242.2	-146.2
56	1,692.0	1,255.0	437.0
57	1,166.0	1,267.9	-101.9
58	1,282.0	1,280.7	1.3
59	1,691.0	1,293.6	397.4
60	938.0	1,306.4	-368.4
61	907.0	1,319.3	-412.3
62	888.0	1,332.1	-444.1