William Gray heads the Tropical Meteorology Project at Colorado State University (well away from the hurricane belt). His forecasts before each year's hurricane season attract lots of attention. Offered are data on the number of named Atlantic tropical storms predicted by Dr. Gray and the actual number of storms for the years 1984 to 2015: Year Forecast Actual Year Forecast Actual Year Forecast Actual 1984 1010 1313 1999 1414 1212 2014 1010 88 1985 1111 1111 2000 1212 1515 2015 88 1111 1986 88 66 2001 1212 1515 1987 88 77 2002 1111 1212 1988 1111 1212 2003 1414 1616 1989 77 1111 2004 1414 1515 1990 1111 1414 2005 1515 2828 1991 88 88 2006 1717 1010 1992 88 77 2007 1717 1515 1993 1111 88 2008 1515 1616 1994 99 77 2009 1111 99 1995 1212 1919 2010 1818 1919 1996 1010 1313 2011 1616 1919 1997 1111 88 2012 1414 1919 1998 1010 1414 2013 1818 1414 To access the complete data set, click the link for your preferred software format: Excel Minitab JMP SPSS TI R Mac-TXT PC-TXT CSV CrunchIt! Analyze these data using the four‑step process. How accurate are Dr. Gray's forecasts? How many tropical storms would you expect in a year when his preseason forecast calls for 1616 storms? What is the effect of the disastrous 2005 season on your answers? STATE: Choose the statement that best describes the question we are trying to answer. Actual number of storms is the explanatory variable and forecasted storms is the response variable. We want to examine whether Dr. Gray's forecasts are reliable. Actual storms is the explanatory variable and percents of storms forecasted by Dr. Gray is the response variable. We want to examine whether Dr. Gray's forecasts are accurate. Forecasted storms is the explanatory variable and actual number of storms is the response variable. We want to examine how far the regression line is from the line y=x.y=x. Forecasted storms is the explanatory variable and actual number of storms is the response variable. We want to examine how accurate Dr. Gray's forecasts are. PLAN: What specific statistical operations does this problem call for? Choose the most appropriate answer. Find the regression equation and the lurking variable. Make a scatterplot, compute the regression equation, and find the value of r2r2 . Make a scatterplot and compute the regression equation. Find the correlation between the explanatory and response variable. SOLVE: The scatterplot of the data is displayed. Choose the statement that best describes your findings. The scatterplot shows a strong negative association. The scatterplot shows a strong positive association. The scatterplot shows a moderate positive association. The scatterplot shows a weak negative association. The relationship does not seem to be linear. Calculate the correlation for the data leaving out the potential outlier year of 2005. Next calculate the correlation r,r, and the regression line parameters, slope bb and intercept a.a. (Enter your answer rounded to three decimal places.) r=r= b=b= a=a= CONCLUDE: Find the percent of the variation in the values of yy that is explained by the least‑squares regression with the outlier removed. Select the correct conclusion. We do not have enough data to assess the accuracy of the predictions of this regression. The regression line is not reliable as a predictor because it explains only 42.5%42.5% of the variation in tropical storms. The regression line is an accurate predictor since it explains 97%97% of the variation in tropical storms. The regression line is an accurate predictor because it explains 65.2%65.2% of the variation in tropical storms. What is the effect of the disastrous 2005 season on your answer? Add back that year's data and refit the model. Consider how many tropical storms you would expect in a year when his preseason forecast calls for 1616 storms. Calculate this for all of the data and for the data without the 2005 values, then choose the correct answer. The prediction for x=16x=16 forecast tropical storms are about 2020 storms with the full data and about 2525 storms without the year 2005. The prediction for x=16x=16 forecast tropical storms are about 1616 storms with the full data and about 1818 storms without the year 2005. The prediction for x=16x=16 forecast tropical storms are about 1717 storms with the full data and about 1616 storms without the year 2005. The regression line without the 2005 season explains a smaller proportion of the variation in storms.

William Gray heads the Tropical Meteorology Project at Colorado State University (well away from the hurricane belt). His forecasts before each year's hurricane season attract lots of attention. Offered are data on the number of named Atlantic tropical storms predicted by Dr. Gray and the actual number of storms for the years 1984 to 2015: Year Forecast Actual Year Forecast Actual Year Forecast Actual 1984 1010 1313 1999 1414 1212 2014 1010 88 1985 1111 1111 2000 1212 1515 2015 88 1111 1986 88 66 2001 1212 1515 1987 88 77 2002 1111 1212 1988 1111 1212 2003 1414 1616 1989 77 1111 2004 1414 1515 1990 1111 1414 2005 1515 2828 1991 88 88 2006 1717 1010 1992 88 77 2007 1717 1515 1993 1111 88 2008 1515 1616 1994 99 77 2009 1111 99 1995 1212 1919 2010 1818 1919 1996 1010 1313 2011 1616 1919 1997 1111 88 2012 1414 1919 1998 1010 1414 2013 1818 1414 To access the complete data set, click the link for your preferred software format: Excel Minitab JMP SPSS TI R Mac-TXT PC-TXT CSV CrunchIt! Analyze these data using the four‑step process. How accurate are Dr. Gray's forecasts? How many tropical storms would you expect in a year when his preseason forecast calls for 1616 storms? What is the effect of the disastrous 2005 season on your answers? STATE: Choose the statement that best describes the question we are trying to answer. Actual number of storms is the explanatory variable and forecasted storms is the response variable. We want to examine whether Dr. Gray's forecasts are reliable. Actual storms is the explanatory variable and percents of storms forecasted by Dr. Gray is the response variable. We want to examine whether Dr. Gray's forecasts are accurate. Forecasted storms is the explanatory variable and actual number of storms is the response variable. We want to examine how far the regression line is from the line y=x.y=x. Forecasted storms is the explanatory variable and actual number of storms is the response variable. We want to examine how accurate Dr. Gray's forecasts are. PLAN: What specific statistical operations does this problem call for? Choose the most appropriate answer. Find the regression equation and the lurking variable. Make a scatterplot, compute the regression equation, and find the value of r2r2 . Make a scatterplot and compute the regression equation. Find the correlation between the explanatory and response variable. SOLVE: The scatterplot of the data is displayed. Choose the statement that best describes your findings. The scatterplot shows a strong negative association. The scatterplot shows a strong positive association. The scatterplot shows a moderate positive association. The scatterplot shows a weak negative association. The relationship does not seem to be linear. Calculate the correlation for the data leaving out the potential outlier year of 2005. Next calculate the correlation r,r, and the regression line parameters, slope bb and intercept a.a. (Enter your answer rounded to three decimal places.) r=r= b=b= a=a= CONCLUDE: Find the percent of the variation in the values of yy that is explained by the least‑squares regression with the outlier removed. Select the correct conclusion. We do not have enough data to assess the accuracy of the predictions of this regression. The regression line is not reliable as a predictor because it explains only 42.5%42.5% of the variation in tropical storms. The regression line is an accurate predictor since it explains 97%97% of the variation in tropical storms. The regression line is an accurate predictor because it explains 65.2%65.2% of the variation in tropical storms. What is the effect of the disastrous 2005 season on your answer? Add back that year's data and refit the model. Consider how many tropical storms you would expect in a year when his preseason forecast calls for 1616 storms. Calculate this for all of the data and for the data without the 2005 values, then choose the correct answer. The prediction for x=16x=16 forecast tropical storms are about 2020 storms with the full data and about 2525 storms without the year 2005. The prediction for x=16x=16 forecast tropical storms are about 1616 storms with the full data and about 1818 storms without the year 2005. The prediction for x=16x=16 forecast tropical storms are about 1717 storms with the full data and about 1616 storms without the year 2005. The regression line without the 2005 season explains a smaller proportion of the variation in storms.

Name: William Gray heads the Tropical Meteorology Project at Colorado State
Uploaded: 2024-03-20T07:06:27.000Z
Channel: Bartleby
Description: William Gray heads the Tropical Meteorology Project at Colorado State University (well away from the hurricane belt). His forecasts before each year's hurricane season attract lots of attention. Offered are data on the number of named Atlantic tropic

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Year	Forecast	Actual	Year	Forecast	Actual	Year	Forecast	Actual
1984	1010	1313	1999	1414	1212	2014	1010	88
1985	1111	1111	2000	1212	1515	2015	88	1111
1986	88	66	2001	1212	1515
1987	88	77	2002	1111	1212
1988	1111	1212	2003	1414	1616
1989	77	1111	2004	1414	1515
1990	1111	1414	2005	1515	2828
1991	88	88	2006	1717	1010
1992	88	77	2007	1717	1515
1993	1111	88	2008	1515	1616
1994	99	77	2009	1111	99
1995	1212	1919	2010	1818	1919
1996	1010	1313	2011	1616	1919
1997	1111	88	2012	1414	1919
1998	1010	1414	2013	1818	1414

To access the complete data set, click the link for your preferred software format:

Excel Minitab JMP SPSS TI R Mac-TXT PC-TXT CSV CrunchIt!

Analyze these data using the four‑step process.

How accurate are Dr. Gray's forecasts? How many tropical storms would you expect in a year when his preseason forecast calls for 1616 storms? What is the effect of the disastrous 2005 season on your answers?

STATE: Choose the statement that best describes the question we are trying to answer.

Actual number of storms is the explanatory variable and forecasted storms is the response variable. We want to examine whether Dr. Gray's forecasts are reliable.

Actual storms is the explanatory variable and percents of storms forecasted by Dr. Gray is the response variable. We want to examine whether Dr. Gray's forecasts are accurate.

Forecasted storms is the explanatory variable and actual number of storms is the response variable. We want to examine how far the regression line is from the line y=x.y=x.

Forecasted storms is the explanatory variable and actual number of storms is the response variable. We want to examine how accurate Dr. Gray's forecasts are.

PLAN: What specific statistical operations does this problem call for?

Choose the most appropriate answer.

Find the regression equation and the lurking variable.

Make a scatterplot, compute the regression equation, and find the value of r2r2 .

Make a scatterplot and compute the regression equation.

Find the correlation between the explanatory and response variable.

SOLVE: The scatterplot of the data is displayed.

Choose the statement that best describes your findings.

The scatterplot shows a strong negative association.

The scatterplot shows a strong positive association.

The scatterplot shows a moderate positive association.

The scatterplot shows a weak negative association.

The relationship does not seem to be linear.

Calculate the correlation for the data leaving out the potential outlier year of 2005. Next calculate the correlation r,r, and the regression line parameters, slope bb and intercept a.a. (Enter your answer rounded to three decimal places.)

r=r=

b=b=

a=a=

CONCLUDE: Find the percent of the variation in the values of yy that is explained by the least‑squares regression with the outlier removed.

Select the correct conclusion.

We do not have enough data to assess the accuracy of the predictions of this regression.

The regression line is not reliable as a predictor because it explains only 42.5%42.5% of the variation in tropical storms.

The regression line is an accurate predictor since it explains 97%97% of the variation in tropical storms.

The regression line is an accurate predictor because it explains 65.2%65.2% of the variation in tropical storms.

What is the effect of the disastrous 2005 season on your answer? Add back that year's data and refit the model. Consider how many tropical storms you would expect in a year when his preseason forecast calls for 1616 storms.

Calculate this for all of the data and for the data without the 2005 values, then choose the correct answer.

The prediction for x=16x=16 forecast tropical storms are about 2020 storms with the full data and about 2525 storms without the year 2005.

The prediction for x=16x=16 forecast tropical storms are about 1616 storms with the full data and about 1818 storms without the year 2005.

The prediction for x=16x=16 forecast tropical storms are about 1717 storms with the full data and about 1616 storms without the year 2005.

The regression line without the 2005 season explains a smaller proportion of the variation in storms.

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