3. NASA's GISS Surface Temperature Analysis (GISTEMP) is an estimate of global surface tempera- ture change recorded monthly. A le, GLB.Ts+dSST.csv, can be downloaded from owl in Data sets folder. It contains monthly temperatures from 1830 to 2020. Please do the following steps to carry out some basic modelings. Any looping such as for, while, repeat is not allowed. {a} Import the dataset into R as a data frame. Create another data frame to keep only Jan, ..., Dec 12 columns. Then use apply mction to generate a vector of yearly average temperatures from 1831] to 2020 and save it as yearlyiemp. Plot it against year=18802202l [as a line] and comment your ndings [any pattern changes]. {13) Construct an objective function based on (sum of square) :{yearlytem a b a: year[]]2 and use nlminb with start values (-10, 0.1] to estimate a, b [saved as ls.est). You cannot use 1111 to nd a, I) though you can use it to check if your answer is right or not. Then compute the residuals as resid=yearly.temp-ls.est[1]-ls.est[2]*year. For model diagnostic checking based on residuals, do the following steps. i. Add the tted line {the tted values computed as tted=ls.est[1]+ls.est[2]*year) as col = 2 to the original yearly temperature plot and comment how good or bad the tted line is. ii. Scatter plot of resid against year and comment out if there are any patterns or it is completely random. iii. Use qqnorm and qqline to resid to see if it is normally distributed. Comment your ndings. (c) Create a dummy vector as dummy: c(rep{,85], rep(1,55]]. Redo (b) with an objective function based on Z{yearly.temp[i] o. h a: year[i] c a: dummy] d a: durnmy] a: yea.r[i])2 i=1 with start values (-1, 1, -1, 1]. For the tted line, choose col = 3. (d) Comment the similarity and difference between the two models. You can overlay two tted lines together in a new plot to comment. Which is the best tted model? What are your conclusions of rising temperature rates per decade? Disclaim: Two models from the above do not take the consideration of yearlyiemp as a time series. Further study is needed for more accurate statistical modelings