DS1000B python 数据分析

Part 1 -- Written Answer (Be sure to show all your work)
Question 1 [12 Points]
The height of elephants are approximately Normal, with a mean of 2.5 metres and standard deviation of 0.5 metres. For each part below, sketch a Normal curve and shade the area representing the region, as well as use Table A to solve.
a. [4 Points] What proportion of elephants have heights greater than 3.5 metres?
b. [4 Points] What proportion of elephants have heights between 2.2 and 3.5 metres?
c. [4 Points] What height must an elephant be to fall in the top 25% of elephants?
Question 2 [13 Points]
The table below gives the self-reported heights of 10 university men (Son's height) along with the heights of their fathers (Father's height), both in inches.

a. [6 Points] Draw, by hand, a scatterplot for this dataset. Comment on the direction, form and strength of this relationship.
b. [5 Points] Find the correlation between the father's and son's height. Show all of your work. Round each calculation to 2 decimal places.
c. [2 Points] Do the value and the sign (positive or negative) of the correlation in part (b) make sense based on the scatterplot from part (a)? Explain.
Question 3 [10 Points]
Consider a study investigating the relationship between husband's height and wife's height in young couples. The mean height of wives (x) in their thirties participating in the study is about 66.2 inches, and the standard deviation is about 3.6 inches. The mean height of husbands (y) the same age is about 75.7 inches, with a standard deviation of about 2.2 inches. Suppose that the
correlation between the heights of husbands and wives is about r = 0.64.
a. [3 Points] What are the slope and intercept of the regression line of the husband's height on the wife's height in young couples? Interpret the slope in the context of the problem.
b. [4 Points] Draw a graph, by hand, of this regression line for heights of wives between 55 and 70 inches. Predict the height of the husband of a woman who is 67 inches tall and plot the wife's height and predicted husband's height on your graph.
c. [3 Points] What percentage of the variation in husband's height is explained by the straight-line relationship with wife's height? Do you expect the prediction made in part b) to be accurate?
Question 4 [10 Points]
Consider a study investigating the relationship between poverty and male life expectancy. Based on the observations in the table below, assume that you have already calculated the regression line to be: y = -0.1824242x + 85.33

a. [4 Points] Use the regression line to calculate the 10 residuals for the observations. What do the residuals add to? Does this make sense?
b. [4 Points] Draw a residual plot. What does this plot tell us about the relationship between our two variables?
c. [2 Points] What is an influential observation? Do you think this dataset contains any?
Part 2 -- Python (Be sure to show all your code and results)
Important Note: Since it is a Python part, without further notice, all numbers and graphs need to be produced using Python by default.
Question 5 [10 points]
The common fruit fly Drosophila melanogaster is the most studied organism in genetic research because it is small, is easy to grow, and reproduces rapidly. The length of the thorax (where the wings and legs attach) in a population of male fruit flies is approximately normal, with mean 0.830
millimeter (mm) and standard deviation 0.075 mm.
a. [2 points] What proportion of flies have thorax length less than 0.7 mm?
b. [2 points] What proportion of flies have thorax length greater than 1.0 mm?
c. [2 points] Explain how you can calculate the proportion of flies with thorax length between 0.7 mm and 1.0 mm. (You can use words/math/diagrams or combination of them. You can write/draw them by hand.)
d. [2 points] Calculate the proportion illustrated in part c.
e. [2 points] What value of thorax length gives a 25% proportion of flies above it?