2. (Four parts; 9 marks in total) Analysis of the trend in global surface temper
ID: 3049191 • Letter: 2
Question
2. (Four parts; 9 marks in total) Analysis of the trend in global surface temperature over time (in years) results in the linear regression model, (Global Temp | Year)--33.07484 0.01 68Year, with the correlation coefficient being r = 0.9351. This analysis is based on data recorded over a 49-year period from 1969 to 2017, inclusive. NOAA based global temperature measurements on surface temperature over land and at sea all over the world, using the average temperature of the 20th century as a baseline. Assume that all the required assumptions for this model are satisfied. a) (2 marks) What percentage of variation in global surface temperature is explained by this simple linear regression model? b) (3 marks) What is the value of the F-statistic used to test if there is any linear relationship? Note: There is sufficient information given above to answer this question. c) (2 marks) what is the value of the test statistic for testing Ho:A-o versus HA: > 0? d) (2 marks) What is the standard error of the estimate of the slope of the regression line?Explanation / Answer
a)% of variation =R2 =(0.9351)2*100 =87.44%
b)
here as F statistic =(n-2)*R2/(1-R2) =(49-2)*0.8744/(1-0.8744) =327.240
c)
value of test statistic t =(F)1/2 =(327.240)1/2 =18.090
d)
stadnard error =estimated slope/t =0.0168/18.090=0.0009
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