4. Interpretation of simple linearregression
The linear model below explores a potential association betweenproperty damage and windspeed based on observational data from 94hurricanes that hit the United States between 1950 and 2012. Thevariables are
Damage: property damage in millions ofU.S. dollars (adjusted for inflation to 2014) for eachhurricane
Landfall.Windspeed: Maximum sustainedwindspeed in miles per hour measured along U.S. coast for eachhurricane
* Assume that the sample data satisfies all assumptionsfor linear regression.
Level of significance = 0.05. Â Â
> summary(model)
Call:
lm(formula = Damage ~ Landfall.Windspeed)
Residuals:
  Min    1QMedian    3Q   Max
-9294 -4782 -1996Â Â -531 90478
Coefficients:
                                              Estimate          Std. Error       t value           Pr(>|t|)
(Intercept)Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â -10041.78Â Â Â Â Â Â 6064.29Â Â Â Â Â Â Â Â -1.656Â Â Â Â Â Â Â Â Â Â Â Â 0.1012
Landfall.Windspeed   142.07           56.65             2.508             0.0139 *
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’1
Residual standard error: 12280 on 92 degrees of freedom
Multiple R-squared: [ A],     Adjusted R-squared: 0.05381
F-statistic: 6.289 on 1 and 92 DF, p-value: 0.01391
(a)Â Â Write the equation for the linearmodel using the variables Damages andLandfall.Windspeed, taking the results of thet-tests into account.
(b) A hurricane is defined as a storm with windspeeds greaterthan 74 miles per hour. Interpret the value of theintercept in connection to the real-life context of thismodel (two or three sentences). Hint: Isthe intercept truly meaningful, given the definition of ahurricane?
(c) The value of Pearson’s correlation coefficient forDamages and Landfall.Windspeed is 0.2529438.Calculate and interpret the value ofR2 , denoted [A] in the table,in relation to the predictor and response variables.
(d) The range of observed maximum windspeeds in the sample datais 75 – 190 miles per hour. Is it appropriate to use the linearmodel to predict the cost of damage for a hurricane with a maximumwindspeed of 150 miles per hour? Why or why not? If so, estimatethe typical value of damages (specifying units).
(e) Would it be appropriate to use the linear model to predictthe cost of damage for a hurricane with a maximum windspeed of 225miles per hour? Why or why not? If so, estimate the typical valueof damages (specifying units).
