hw2 - 10. a. 1.08 z= 23.84-20/3.56 = 1.08 b. 10 because z =...

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Unformatted text preview: 10. a. 1.08 z= 23.84-20/3.56 = 1.08 b. 10 because z = 34-23.84/3.56 = 2.85 vs z = 10-23.84/3.56 = 3.89 12. a. 23.84-20 = new mean = 3.84, the s would be unchanged at 3.56 b. mean = 38.35, new s = 5.73 14. Mean = 28*10 + 100 = $380 Max = 33*10 + 100 = $430 Std = 2.4*10 = $24 IQR = 3.2*10 = $32 6.28 a. the median, there are a lot of outliers in this graph that have a large effect on the mean, and may create a bit of distorted summery of the data. The median simply takes the middle value so it is not as sensitive to outliers b. the IQR for the same reason as above, the IQR is less sensitive to outliers, where as the s is not. c. 68% - 340 d. approx 30% 150 btw 71-95 e. this is not a normal distribution because there are many outliers and the fact that most of that data is concentrated in the 95-100 percent range. Thus, data within one standard distribution of the mean does not contain 68 percent of the data taken in the survey. 7.14 a. yes, this graph shows a strong linear correlation with one slight outlier at the end. b. there is a strong positive linear correlation between drug improvement and placebo improvement, showing that on average, patients improved while taking both drugs, but more dramatically when taking the real drug vs the placebo. 7.8 There is moderately strong positive correlation between the year a horse raced and its winning speed. However, past year 1950 the positive correlation decreases to almost zero and becomes stronger showing that horses past this period in time showed little to no increases or decreases in their winning speeds as the year progressed past this period. 7.26 a. not necessarily, people who own cell phones may tend to live longer than those who do not but this does not imply that owning a cell phone actually increases your life expectancy. b. people who own cell phones may tend to have more money than those who do not because a cell phone, thus those who own cell phones may have more money to pay for health care, lodging or food, and these things may relate to life expectancy. 8. a. I would expect that the there would a positive correlation between duration and length and a negative correlation between duration and speed. I would expect that a longer length rollercoaster would take longer to finish because it would take longer to complete the course, and one that had cars that moved quickly to be short in duration because it would cover ground more quickly. b. 1000 3000 5000 7000 | | 7000 ||| | || || || |||||| | ||| | ||| | | | || | Length 1000 3000 5000 | || | | |||| | | || |||| ||| | ||||| || | | | | | 120 ||| | | | | || | || |||| |||||| | | | | | | 100 | 120 50 100 150 200 40 60 80 Duration Length Speed Duration 1.0000000 0.7584662 0.1189838 Length 0.7584662 1.0000000 0.3752975 Speed 0.1189838 0.3752975 1.0000000 40 60 80 100 Speed 50 100 150 200 Duration The correlation matrix and the scatter plot matrix both shows that there is a high strong positive correlation between duration and length as expected, but there is a low weaker correlation between duration and speed. c. mean sd 0% 25% 50% 75% 100% n y = Duration 138.90323 45.92214 17 111 141.5 180.000 240 62 x = Length 3769.04468 1462.53356 635 2658 3851.0 4994.753 7400 62 x = Speed 65.46452 13.79339 40 55 65.0 72.750 120 62 b1,L = r*(Sy/Sx) = .76* (45.922/1462.533) = 0.0239 b1,S = = .12*(45.922/13.79) = 0.3996 bo, L = y b1*x = 138.9 - .0239(3769) = 48.8209 bo, S = = 138.9 - .3996*65.46 = 112.742184 y = 48.82 + .0239L y = 112.74 + .3996S R^2 = .76^2 = .5776 57.76% = .12^2 = .014 The better predictor of duration is length. The least squares line is y = 48.82 +.0239L, meaning that roller coasters are about .0239 seconds longer per unit length of the coaster. And that the average length of a coaster that is zero units long would average 48.82 seconds long. R^2 shows that 57.76% of the variability in duration is accounted for by the length of the coaster. 9. a. taller children may be better readers, but this does not imply that being taller makes a child better at reading b. Taller children may tend to be older, and older children who have had a better education may be able to read better than those who are smaller and tend to be younger and have had less education. 10. a. the strongest correlations with Pct BF are chest, hip, waist, and weight, ranging from . 61-82. None of these come as too much of a surprise because theses are all places in the body that would tend to store body fat or imply that a person has a higher body fat content. I am not familiar enough with how the body stores fat throughout the body to draw any conclusions about these body parts and their relations to Pct BF, other than a fatter person would tend to have larger body parts. Age however did not have as strong or consistent correlations with other variables. The strongest were -height, pct bf, -thigh, waist, and wrist. These correlations range between the -.24 and +.29. What I find surprising about these correlations is that it is ambiguous as to what body parts grow and shrink as a person's age goes up. A person's height decreases and body fat seems to increase, which seems to account for why a person's waist and wrist size increase, but not as to why a person's thigh size would decrease. I would expect a person whose body fat was increasing to also have increases in their thigh size. Age Age 1.00000000 Ankle -0.10961619 Bicep -0.04414096 Chest 0.18181484 Forearm -0.08511618 Height -0.24588654 Hip -0.05813360 Knee 0.01719386 Neck 0.11873841 Pct.BF 0.29505077 Thigh -0.21608381 Waist 0.24278001 Weight -0.01605487 Wrist 0.21750640 Pct.BF Age 0.29505077 Ankle 0.24455555 Bicep 0.48153820 Chest 0.70066962 Forearm 0.36470886 Height -0.02938959 Hip 0.63267468 Knee 0.49230767 Neck 0.48852424 Pct.BF 1.00000000 Thigh 0.54854962 Waist 0.82368465 Weight 0.61729944 Wrist 0.33900781 b. waist size seems to be the best predictor of PctBF. It is the strongest scatter plot with few to no outliers, and it has a largest correlation value of .82. 64 70 76 50 60 70 16 18 20 20 40 60 80 Age |||||||||||||||||||||||||||||| | ||||| ||||| || || | ||| Height |||||||||||||||||||||||||||| | || || |||||||| |||| 64 70 76 Pct.BF |||||||||||||||||||||||||||||||| || | | |||||||| || || || || || || Thigh | ||||||||||||||||||||||||||||||| | | || ||||| || ||||||| 50 60 70 | ||||||||||||||||||||||||||||| | | |||||||||||| ||| || || 20 Wrist ||||||||||||||||||||||||||| | | |||||| ||| ||| |||| || || 16 18 Weight |||||||||||||||||||||||||||||||| | ||||||| |||| || ||| || || ||| || || 20 40 60 80 0 20 40 30 40 50 150 250 c. the correlation between PctBF and Height is -0.02938959, and the scatter plot below suggest that there is no correlation between Height and PctBF. The correlation is almost zero and there is no strong trend in the scatter plot. 150 250 30 40 Waist 50 0 20 40 Pct.BF 0 64 10 20 30 40 66 68 70 Height 72 74 76 78 d. when looking at the 3d scatter plot, the correlation between height and Pct BF seems stronger than one in the 2d scatter plot. I believe however that this is due to the fact that the y axis on the Pct BF is not oriented in a single plane when trying examine the slope of the best fit. This seems to suggest that the way the 3d graph displays information can overemphasizes the visual correlations between variables. ...
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This homework help was uploaded on 10/07/2007 for the course ORF 245 taught by Professor Richardd.deveaux during the Spring '07 term at Princeton.

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