The Consumer Reports New Car Buying Guide contains lots of information for a large number of new car models. Some of the data for 110 of these cars has been extracted. This project will focus on the relationships among several of these variables including:
Weight = Weight of the car (in pounds)
CityMPG = EPA’s estimated miles per gallon for city driving
FuelCap = Size of the gas tank (in gallons)
QtrMile = Time (in seconds) to go 1/4 mile from a standing start
Acc060 = Time (in seconds) to accelerate from zero to 60 mph
PageNum = Page number on which the car appears in the buying guide
Tasks:
- Initial guesses (BEFORE looking at the data)
Consider the relationship you would expect to see between each the following pairs of variables for the car data. Place the letter for each pair on the chart below to indicate your guess as to the direction (negative, neutral, or positive) and strength of the association between the two variables. Note: You may have more than one letter at about the same spot.
(a) Weight vs. City MPG (d) Weight vs. QtrMile Time
(b) Weight vs. Fuel Capacity (e) Acceleration 060 vs. QtrMile Time
(c) Page Number vs. Fuel Capacity (f) City MPG vs. QtrMile Time
Strong
Moderate
Weak
No
Weak
Moderate
Strong
Negative
Negative
Negative
Association
Positive
Positive
Positive
2 Associations from scatterplots
Use matrix of scatter plot to examine the various pairs of car variables listed above.
Revise your estimates on the direction and strength of each association in the chart below.
How did you do with your initial guesses?
Strong
Moderate
Weak
No
Weak
Moderate
Strong
Negative
Negative
Negative
Association
Positive
Positive
Positive
- Compute correlations for each pair
The correlation coefficient, denoted by r, is a measure of the strength of the linear association between two variables. Use technology (or values supplied by your instructor) to find the correlation for each of the six pairs of variables, (a) – (f), and record the results in the table (two decimal places is fine).
correlation
correlation
(a) Weight vs. CityMPG
(d) Weight vs. QtrMile
(b) Weight vs. FuelCapacity
(e) Acc060 vs. QtrMile
(c) PageNum vs. Fuel Capacity
(f) CityMPG vs. QtrMile
4 Properties of correlation
Based on your observations of the scatterplots and computed correlations, write down at least three properties that would appear to be true about a sample correlation and its interpretation.
(1)
(2)
(3)
Sample Solution
Before delving into the world of FDR as president, one must understand FDR the governor. During his time as governor of New York, FDR had developed a reputation for himself, one of a man who is willing and ready to back liberal reforms. This was mainly due to his abolishing of the death penalty, the support the provided to pensioners and farmers alike, as well as his readiness to allocate more money for schools. However, FDR also developed a not so friendly relationship with the elites of the democratic party, they viewed him as someone who lacked a backbone. This reputation allowed FDR to establish himself as a humble man, one who would openly seek advice from those perhaps better educated on a certain topic. For example, FDR was the first president to seek advice from university professors, an all too often underused resource in society. This allowed FDR to better connect with the average American, something he excelled at due to his relentless news bureau, radio interviews, and his press conferences. However, without a doubt, despite all of the successes enjoyed by FDR during his time as governor of New York, the greatest crisis he faced was the Great Depression. Despite not entirely understanding exactly how to make it better, FDR understood the realities of the situation, as well as the need to pragmatic. By 1931 there were over 800,000 unemployed people in New York. FDR most definitely preferred the practical, but he also believed in the concepts of progress and the important role the state held in thing care of its citizens. Therefore, in response to the effects of the Great Depression, FDR created the Temporary Emergency Relief Administration (TERA) with an initial appropriation of $20 million targeted for the emergency relief of the unemployed. Able-bodied workers without jobs would get relief from the state—first home (direct) relief and then the more desirable work relief. Roosevelt thus set a precedent by creating a new agency to meet a new problem, one he relied on during the New Deal years. Hopkins concentrated on creating a program in New York State that could set an example for other states. This was important, he believed, because the TERA represented “the first enactment under which a State, as such, had accepted any liability for the support of its population, viewed not as wards but merely as men and women unable temporarily to accommodate themselves to the social scene, with-out at the same time placing such men and women in the position of recipients of a bounty or a dole and in such a manner as to preserve the self-respect of every beneficiary. . .” De>
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