Assignment 5

1975 1980 1985 1990 1995 2000 2005 2010 2015 2020 2025 0 1 2 3 4 5 6 7 8 9 f(x) = − 0.08 x + 168.44 R² = 0.79 September Sea Ice Extent (1,000,000 sq km) Year September Sea Ice Extent (1,000,000 sq km) 2. Plot a scatter plot of the data. In your own words, describe the data. The data seems to be on a down trend. 3. Fit a linear trend to the dataset. Based on the linear trend, what is the rate of change of the Arctic sea ice? What is the intercept? What is the R2 value for this trend? The rate of change is -8.12*10^-2 (1,000,000 sq km) per year.The intercept is 168.44. The R- squared value is .7935 4. Based on the rate calculated in question 3. When do you think that Arctic Sea Ice area will reach zero? Discuss any issues that may occur with these types of models (is it realistic? Why or why not?) Based on the model, the artic sea ice area will reach zero in 2074. I believe the model is realistic if no action is taken to control the loss. This is a good model to show us what will happen if action isn't taken soon. 5. Using the "Regression" function (instructions provided in assignment 4) calculate an error on the slope and the intercept . The standard error on the intercept is 12.9 and the standard error on the slope is 6.47*10^-3 6. Calculate the predicted data and the residuals from your fit. Plot the residuals on a scatter plot. What do you observe about the residuals? Comment on the goodness of fit. Provide the graph in your write up. The residual seem to be scattered which indicated that the equation is a good fit for this data.

1975 1980 1985 1990 1995 2000 2005 2010 2015 2020 2025 -1.5 -1 -0.5 0 0.5 1 1.5 2 Residuals Year Residual 7. Plot a histogram of the residuals. What do you observe about the histogram of the residuals? Comment on the goodness of fit. Provide the graph in your write up. That most of the residuals are in the middle of the histogram which indicated that they are very close and there are very few "outliers" 8. To examine why, fit a linear trend to the data from 1979 to 2001 and compare it to a linear trend to the data from 2002 to 2021. What are the rates of change for these time periods? What are the intercepts? What are the R2 values? Compare the rates to the rate determined in question 3 and comment. Based on these two new fits, why is the consensus view of the melt rate of Arctic sea ice changing? Provide the graph in your write up.

For the first time period, the rate of change is -3.99*10^-2, the intercept is 86.384, the R- squared is .2924. For the Second time period, the rate of change is -7.26*10^-2, the intercept is 151.08, and the R-squared is .4014. The rate of change of the first time period is a lot farther than the second time period. The consensus view is changing probably because we have been accelerating the melting in the past 20 year at almost double the rate than we have in the past. 1975 1980 1985 1990 1995 2000 2005 2010 2015 2020 2025 0 1 2 3 4 5 6 7 8 9 f(x) = − 0.07 x + 151.08 R² = 0.4 f(x) = − 0.04 x + 86.38 R² = 0.29 First half vs second half Year Resiudal 9. Plot the residuals for your two new trends. What do you observe about the residuals? Provide the graph in your write up. The residuals look evenly distributed above and below zero which makes them a good fit. 1975 1980 1985 1990 1995 2000 2005 2010 2015 2020 2025 -1 -0.5 0 0.5 1 1.5 2 First half vs second half resiudals Year Residual