Linear Regression Line

The Barbie Bungee lab was conducted in order to find the association between the amount of rubber bands and the distance the Barbie bungeed. Before performing the final experiment, the group conducted an initial investigation to get data that could be analyzed to examine the comparison from the amount of rubber bands to the length Barbie was able to bungee. In the investigation rubber bands would gradually be added one by one starting at two rubber bands. Each time a rubber band was added, three trial bungees were done and the lengths the barbie dropped were recorded. Using data collected from our background investigation, the group used excel to create a sheet displaying the data in a table, a graph showing the correlation constant, the line of best fit. The line of best fit was in slope-intercept form (y=mx+b) where y represents the length of the trial average; m represents the slope

* Correlation coefficient (R-squared) – This represents how well the independent variables (X) explain the response variable (Y).

There has been a major correlation between the rate of crime and citizens shown throughout the nation.

Because of the method of monthly data collection, absolute randomness could not be obtained; however, it was decided that 5 iterations was sufficient because the sixth iteration showed a decrease in the quality of the residual plots. The first test performed was the p-value test of the individual variables. A p-value is the probability, ranging from 0 to 1, of obtaining a test statistic similar to the one that was actually observed. The only input that did not have a p-value less than 0.05, which was the chosen significance level, was the “Number of Walmarts” variable; the number of Walmarts has no specific effect on the output, property crime rate. The R2 of the analysis, or the coefficient of determination, provides a measure of how well future outcomes are likely to be predicted by the model. R2 values range from 0 to 100% (or 0 and 1) and the

Although crime has been around for ages, we only started collecting crime data around the 1930’s. Crime statistics show a lot about a country, state, county, etc. Crime can be linked to the environment, behavior of others, and personal experiences, it all depends on how the person deals with the hand they are dealt. Crime data is collected from three sources, which are uniform crime reports (UCR), national incident based reporting system (NIBRS), and national crime victimization survey (NCVS).

6. Why is the black line so much more variable than the red line? What 's the difference between the data they show?

Feedback: A strong correlation exists when the plotted ordered pair points are close to the line of best fit. If the points line up exactly on the line of best fit, there is a perfect correlation. The

Looking back to 1960 we can notice that violent crime rates always vary. In 1960 murder was at 824, but the 1961 it dropped to 788, then goes back up to 983 in 1966. There is no real pattern to how it varies. Many might think that with increased population we will have increased crimes, but that isn’t the case. In 1975 the population was an approximate 12,237,000 and violent crime was at 1,639. In 1976 the population grew to 12,487,000 but the violent crime dropped to 1,519. (4)

In chapter 4 the chapter considers a variety of possible explanations for the significant drop in crime and crime rates that occurred in the 1990s. Based on articles that appeared in the country’s largest newspapers, the authors compile a list of the leading, commonly offered explanations. The next step is to systematically examine each explanation and consider whether available data support the explanation. What the authors, in fact, demonstrate is that in all but three cases–increased reliance on prisons, increased number of police, and changes in illegal drug markets–correlation was erroneously interpreted as causation and in some cases, the correlation wasn’t even that strong.

Based on my interpretation of the reading, higher crime rate themselves has lowered crime rates. Base on many studies conducted and funded by the U.S. department of justice there has been a relationship between the incarceration and crime. Research has founded that reduced crime rates are associated with increase imprisonment rates. On the other hand, increase in crime rate are associated with a decrease in imprisonment rates. Based on this, I would have to say that higher incarceration rates had reduce crime rates.

A third threat to validity is the possibility that results are caused by natural fluctuations in crime rates that would occur without any interference from crime prevention strategies. To combat this problem Ditton and Short have compared the crime rates of the areas under surveillance, to other places in the

This states that 18.1% of the variation in crime rate is explained by regression of education on crime. Since this value is not close to 1, it doesn’t seem to be a appropriate predictor to determine the crime rate in USA.

The study revealed that crime rates are reduced by several factors. The consultant presented the following table which includes each factor and its beta coefficient. During the meeting the Captain sitting next to you turns to you and whispers, “I can’t make heads or tails of this statistics stuff. Which factor appears to have the most effect on reducing the crime rate?”

The trendline, known as the line of best fit or the least squares regression line, shows the linear equation which best explains the sums up the data’s trend. The formula on the right is the formula of the line of best fit.

Determine whether the correlation is significant Calculate and interpret the simple linear regression equation for a set of data Understand the assumptions behind regression analysis Determine whether a regression model is significant