Course: Statistics and Data Analysis

Part A

How big is a granule of sand? It was often thought that the only real predictor was the wave energy. However, it was thought that the slope of the beach might play a role as well. In particular, the steeper the beach, the larger the granules tend to be.

Shown here are results taken from 9 beaches. In each beach, the average granule size was measured.

Steepness:

0.629999995, 0.699999988, 0.819999993, 0.879999995, 1.149999976, 1.5, 4.400000095, 7.300000191, 11.30000019

Granule Diameter:

.170000002, 0.189999998, 0.219999999, 0.234999999, 0.234999999, 0.300000012, 0.349999994, 0.419999987, 0.850000024

To clarify, for Beach #1, the steepness gradient was 0.6299 and the average granule diameter was 0.17. For Beach #2, the steepness was 0.699 and the average granule was 0.189, etc.

Go through the regression process as described in lectures and generate a model in which you predict the granule size from the steepness of the beach. Of course, you should only do this after doing some basic checks on each variable separately.

As always, as a data analyst, you should provide a brief discussion of what you find. That is, imagine you are providing this analysis to someone who has to make policy decisions, yet has no background in statistics. Try to describe your regression model in real world. Part of this kind of discussion should always include how strong or not strong you believe the model to be.

Part B

Shown here is some data representing poverty rates and teen birth rates. Each observation is from a different state. The poverty rate means the percentage of people in that state who live below the poverty line. The birth rate means the number of births (for every 1000 people) among teenagers.

Here are the observations:

Teen birth rate (per 1000 teens):

54.5, 39.5, 61.2, 59.9, 41.1, 47, 25.8, 46.3, 69.1, 44.5, 55.7, 38.2, 39.1, 42.2, 44.6, 32.5, 43, 51, 58.1, 25.4, 35.4, 23.3, 34.8, 27.5, 64.7, 44.1, 36.4, 37, 53.9, 20, 26.8, 62.4, 29.5, 52.2, 27.2, 39.5, 58, 36.8, 31.6, 35.6, 53, 38, 54.3, 64.4, 36.8, 24.2, 37.6, 33, 45.5, 32.3, 39.9

Percentage of People in the State Living in Poverty

20.1, 7.1, 16.1, 14.9, 16.7, 8.8, 9.7, 10.3, 22, 16.2, 12.1, 10.3, 14.5, 12.4, 9.6, 12.2, 10.8, 14.7, 19.7, 11.2, 10.1, 11, 12.2, 9.2, 23.5, 9.4, 15.3, 9.6, 11.1, 5.3, 7.8, 25.3, 16.5, 12.6, 12, 11.5, 17.1, 11.2, 12.2, 10.6, 19.9, 14.5, 15.5, 17.4, 8.4, 10.3, 10.2, 12.5, 16.7, -1.5, 12.2

Note: The first value in each set of observations refers to a state. So, the 54.5 you see refers to Alabama in this case, and indicates that there are 54.5 births per 1000 people. The corresponding 20.1 indicates that 20.1% of individuals in Alabama live below the poverty line. Similarly, the next number in each set of observations (which happens to correspond to Alaska), shows 39.5 births per 1000 people, and 7.1% living below the poverty line.

You would like to see if the percentage of people living in poverty can be predictive of the teen birth rate.

Generate a regression model with birth rate as the response variable, and poverty as the explanatory variable. Of course, you should only do this after doing some basic checks on each set of observations separately (hint hint).

As always, as a data analyst, you should provide a brief discussion of what you find. That is, imagine you are providing this analysis to someone who has to make policy decisions, yet has no background in statistics. Try to describe your regression model in real world. Part of this kind of discussion should always include how strong or not strong you believe the model to be. As a friendly hint, note that there is one numeric value in particular that should give you a sense of the strength of the model.

As part of your discussion, also be sure to answer the following questions:

Do you think any observations should be removed? That is, are there any outliers or influential points that you believe have an undue influence on the model?

Does the model seem to indicate that poverty is a good predictor with the birth rate?