For this question, we will utilize the data in "treadmill.csv". We've provided documentation for this dataset, including a description of how the data was collected and a list of the variables. The .csv file is missing variable names, so we must add these when reading in the data. Here is code to load the data into R: treadmill <- read.csv("treadmill.csv", col.names = c("case", "duration","VO2max","rate", "age", "height", "weight"),header=F) # note that VO2max is named using the letter O, not the number zero (0) We will be looking at the relationship between VO2max, which is the maximum oxygen consumption per minute normalized by a patient's weight (measured in ml/kg/min), and duration (measured in seconds). The goal of the following analysis is to investigate the association between VO2max level and the duration spent on treadmill (measured in seconds). a. Create a scatter plot of VO2max (y-axis) versus duration (x-axis). (Hint: see lab 9) b. Based on the scatter plot, describe the relationship between VO2max and duration. Does there appear to be an association? c. What is the correlation between VO2max and duration? Estimate the (Pearson) correlation coefficient, using the "cor" function in R. What do you conclude about the association of duration with VO2max? (Hint: see lab 9) d. Write the regression equation for a (simple) linear regression model with VO2max as the outcome (dependent) variable and duration as the predictor (independent) variable. e. Fit the linear regression model in part d. Report coefficient estimates for the intercept () and the slope (), and the 95% confidence interval for the slope. What is the scientific interpretation of the estimated coefficient of the variable duration ()? (Hint: see lab 9) f. State the null and alternative hypotheses for testing that the slope (1) is zero (use a significance level of = 0.05). Report the p-value for the test and interpret the statistical conclusion. g. What do you conclude about the association of duration spent on treadmill with VO2max? Include your statistical and scientific conclusions.

1	706	41.5	192	46	165	57
2	732	45.9	190	25	193	95
3	930	54.5	190	25	187	82
4	900	60.3	174	31	191	84
5	903	60.5	194	30	171	67
6	976	64.6	168	36	177	78
7	819	47.4	185	29	174	70
8	922	57	200	27	185	76
9	600	40.2	164	56	180	78
10	540	35.2	175	47	180	80
11	560	33.8	175	46	180	81
12	637	38.8	162	55	180	79
13	593	38.9	190	50	161	66
14	719	49.5	175	52	174	76
15	615	37.1	164	46	173	84
16	589	32.2	156	60	169	69
17	478	31.3	174	49	178	78
18	620	33.8	166	54	181	101
19	710	43.7	184	57	179	74
20	600	41.7	160	50	170	66
21	660	41	186	41	175	75
22	644	45.9	175	58	173	79
23	582	35.8	175	55	160	79
24	503	29.1	175	46	164	65
25	747	47.2	174	47	180	81
26	600	30	174	56	183	100
27	491	34.1	168	82	183	82
28	694	38.1	164	48	181	77
29	586	28.7	146	68	166	65
30	612	37.1	156	54	177	80
31	610	34.5	180	56	179	82
32	539	34.4	164	50	182	87
33	559	35.1	166	48	174	72
34	653	40.9	184	56	176	75
35	733	45.4	186	45	179	75
36	596	36.9	174	45	179	79
37	580	41.6	188	43	179	73
38	556	22.7	186	54	180	75
39	497	31.9	168	55	172	71
40	605	42.5	174	41	187	84
41	552	37.4	166	44	185	81
42	640	48.2	174	41	186	83
43	500	33.6	180	50	175	78
44	603	45	182	42	176	85