What is the R-square value for the regression model?
Description
Criminal justice agencies are often interested in determining whether certain characteristics or variables of offenders can predict certain outcomes. For instance, recidivism, which is defined as the return to prison after being released, is often looked at in terms of what variables predict that outcome. Variables such the following can influence recidivism:
Race
Gender
Criminal history
Treatment received
For this Individual Project, you are working as an analyst for a state correctional agency. You have been asked to investigate whether or not the number of drug arrests an individual has predicts their number of prison incarcerations. These data will be used to shape a sentencing policy.
This assignment has three steps.
Step 1: This assignment will require you to complete the linear regression using Microsoft Excel and to interpret the results of that analysis. Before you do that, view the following video and Web site on residuals and residual plots because there will be questions about this later:
Video: Residual Plots
Web site: Residual Analysis in Regression
Step 2: Transfer the data from the following table into Microsoft Excel.
SUBJECT # DRUG ARRESTS (X) # PRISON INCARCERATIONS (Y)
1
7
3
2
10
4
3
3
1
4
5
4
5
5
4
6
6
2
7
9
6
8
8
5
9
4
1
Then, use the following data analysis part of Excel to conduct the regression (follow the given steps).
The following are the steps to conduct regression in Excel:
Cut and paste these columns of data into an Excel sheet.
Go to the Data tab, and click the Data Analysis button to open the dialogue window. Highlight “Regression,” and click “OK.” This tells Excel that you will be calculating a regression model.
When the Regression dialogue opens, it will require inputs. First, click on the Input Y Range box, and then use your cursor to select all of your values that are in the Y column. This tells Excel what data to consider as the response variable. Make sure that the dotted line encompasses the entire column to include the label header (# prison incarcerations).
Next, click on the Input X Range box, and select all of the values that are in the X column. This tells Excel which data to consider your explanatory variable. Again, make sure that the dotted line encompasses all of the column to include the header (# drug arrests).
Next, click on the Labels box and then the New Worksheet Ply button, and Type “Output” in the box next to that button. This tells Excel to read the labels of your columns as names and not data and to place the output of the analysis on a new worksheet.
Then, click the Residuals box and the Residual Plots box. This tells Excel to analyze the residuals for the regression line and to plot them on a graph, giving you a visual idea of how far away each point of your data is from the predicted values given by the regression equation.
Once done, click “OK” to run the analysis.
Step 3: Now that you have conducted the analysis, answer the following questions:
What is the R-square value for the regression model?
What does the R-square value tell you about the regression model?
What is the significance F value of the model?
What does the significance F value tell you about the statistical significance of the model?
What is the coefficient (t stat value) for the X variable drug arrests?
What does the coefficient (t stat value) mean? In other words, how do you interpret the coefficient?
What is the p-value for the X variable drug arrests?
What does the p-value for drug arrests tell you about its ability to predict prison incarcerations at a level of statistical significance?
Is the residual plot a random pattern, a nonrandom U pattern, or an inverse U pattern? What does the type of pattern tell you about the fit of the regression model to the data? i got this so far Here are the numbers you provided for drug arrests (X): [7, 10, 3, 5, 5, 6, 9, 8, 4] And here are the numbers for prison incarcerations (Y): [3, 4, 1, 4, 4, 2, 6, 5, 1] Now, im going to use something called linear regression. It’s a fancy name, but all it means is we’re trying to draw a straight line that best fits our numbers. This will help me understand the relationship between X and Y. 1. R-square Value: This is a way to see how well our line fits the data. The closer the R-square value is to 1, the better our line fits. If it’s closer to 0, it’s not a good fit. So, higher numbers are what I am looking for! 2. Significance F Value: This number helps us see if there’s a real connection between drug arrests and prison incarcerations. If this number is really small, like less than 0.05, it means our findings are likely not just by chance. 3. Coefficient for X: This number tells us how Y (prison incarcerations) changes when X (drug arrests) changes by one unit. If the number is positive, it means as drug arrests go up, prison incarcerations also tend to go up. If it’s negative, it means the opposite. 4. p-value for X: A small number (again, usually less than 0.05) means that our results are statistically significant. 5. Residual Plot: After we make our line, we’re going to have some leftover data, which we call residuals. We plot these residuals to see any patterns. – A random pattern means our line fits the data pretty well. – A U shape means we might be missing something in our data or our line isn’t the best fit. – An upside-down U shape tells us that our straight line might not be the best choice to describe the data.
Requirements:
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