PubHlth 391B: Homework 6Due by 9 am on Monday Dec 7, 2015Sungho YoonInstructions: Use the Fitness.csv dataset to answer the following questions. These questions may be answered using R or any other software package. Your document should have each question followed by the answer. You will NOT receive full credit if you do not list the questions and the respective answers sequentially. After completing the assignment, upload your answers on Moodle as a Word or PDF file (lastname_hw6.docx or lastname_hw6.pdf) The final date to submit this assignment and receive full credit is before the beginning of class on Dec 7th, 2015. The final day to submit the assignment for partial credit (-20%) is by the beginning of class, Dec 9th, 2015. Exercise: We would like to investigate whether there is a linear relationship between age and VO2 using the Fitness dataset. Specifically, we hypothesize that as age increases, the VO2 value decreases. a. (3 points) Determine the correlation coefficient, r, between age and VO2 and answer the following questions: (i) Is this association strong or weak? - This association is weak because the correlation is – 0.178.(ii) Is this association positive or negative? - The association is negative because correlation is also negative.b. (5 points) Provide a scatterplot and the least squares regression line using technology (Make sure to also check the assumptions and comment on whether or not any are satisfied. Include all relevant output) X = age, Y = VO2Assumption - Linearity Data is linear, appeared to be scattered.In histogram of age- Not normal residuals, unusual observation that do not follow trend. (Demonstrated by histogram) - It is not constant variability because the graph does not normally distributed - It is random sample because data are from the individualIn histogram of VO2- It is normal residuals, because vo2 is normally distributed - It is constant variability because it is normally distributed- It is random sample because data are from the individualThis is for ageThis is for VO2c. (2 points) What VO2 value does the least squares regression line predicts for a person that is 40 years old? - Y = mx + B M = slope, B = Intercept, X = age , Y = VO2M =-0.176, B = 44.931, X = 40, Y = (-0.176)* 40+ 44.931 = 37.891 Ml/kg/mind. (2 points) Provide an interpretation of the slope coefficient in the context of age and VO2. - As age increases one unit, VO2 decreases 0.176e. (3 points) What proportion of the variability in VO2 values is unexplained by the least squares regression line using age as the predictor variable? - (1 – r^2) is the proportion of the variability in VO2 unexplained by the least squares regression line using age. 1 - (-0.176)^2 = 0.969024 = 96.9%f. (5 points) List one other variable (it does not have to be in this dataset) that may account for some of this unexplained variability and explain why you think it is an important variable to predict VO2.- Exercise variable, how much I need to be do exercising.If I do regular exercise, lung capacity is going to go up, and it could possibly increase the VO2. More specific example is that measure of duration of running per