2. (Four parts; 9 marks in total) Analysis of the trend in global surface temper
ID: 3062602 • 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 1 Year)--330748 + 0.01 68Year, with the correlation coefficient being 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 H0: ,-0 versus H. A > 0? d) (2 marks) What is the standard error of the estimate of the slope of the regression line 3. (Three parts; 6 marks in total) The gestation time (time) between fertilization and birth for a mammal is related to the birth weight (weight) by the relationship, (In(time)! weight) = + weight . The approximate gestation time and birth weights (in kg) of 11 selected mammals were recorded. The least squares estimate of the regression line was observed to be (In( time) l weight)-5.231 + 0.01 1 weight . Assume all the required assumptions for this model are satisfied a) (2 marks) On the original scale, estimate the difference in gestation time for mammals with birth weights that differ by 1 kg b) (2 marks) A 95% confidence interval for the slope of this regression line is (0.006, 0.016). Interpret this confidence interval on the original scale c) (2 marks) A 95% prediction interval for the natural log of gestation time of a lion that weighs 1.2 kg at birth is (4.59, 5.90). Interpret this prediction interval on the original scale. 4. (4 marks) Single-factor ANOVA and simple linear regression analysis both have assumptions about normality and equal standard deviations. However, the specific requirements regarding these assumptions differ in these two cases. Therefore, for each of these two types of analyses, explain what the specific requirements are for the assumptions mentioned.Explanation / Answer
The assumptions of Single factor ANOVA:
1.The response variable residuals are always normally distributed
2. The variances of the populations under consideration are equal
3.The responses of a given group are independent, identically distributed random variables
Assumptions of Simple Linear Regression
1.There should be a linear relationship between the x and y variables
2.There must be a normal distribution of the data points
3.T here must be very little or no multicollinearity in the data
4.There should be any autocorellation present in the data
5.There should be no heteroscadasticity ie the variances should be uniform through out the data
The above points are the differences in the assumptions made in the 2 models ie Single factor ANOVA and Simple linear regression
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