Discussion Question #11: Bivariate Correlation and Regression
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- Write a few sentences comparing bivariate correlation and bivariate regression. You need to discuss when it is appropriate to use each of these statistics.
- Interpret the following correlation coefficients
- -.55 between the crime rate in a neighborhood and the median income level per household.
- .17 between the number of hours spent working after school and self-report delinquency.
- Is there a relationship between the number of juveniles arrested for violent crimes and the unemployment rate? A student ran a correlation analysis in SPSS and got the following results:
What would a two-tailed hypothesis test (with alpha – .05) using this data show about the relationship between the two variables? Justify your conclusions.
Q4. Kyung-Shick Choi, Mitch Librett, and Taylor Collins (2014) found that a gunshot detection system, Shotspotter™, significantly reduced the time it took police to respond to a gun-related crime. You are interested in determining whether this faster police response time (x) will lower the crime rate (y) in a given community and, conversely, whether a longer response time is associated with a higher crime rate. You have a small SPSS dataset with the average time it takes the police to respond to a call by a citizen for help in a community as well as that community’s rate of crime. With these data, do or answer the following:
- Draw a scatterplot of your data points.
- Calculate what the slope of the regression line would be.
- Determine what the y intercept is.
- What is the predicted rate of crime (y^) when the police response time is 11 minutes?
- Calculate the value of r and determine whether it is significantly different from zero with an alpha level of .05.
- How much of the variation in the rate of crime is explained by police response time?
- What would you conclude about the relationship between police response time and crime?
A few things: Where it says “calculate” you will run the appropriate analysis in SPSS using the dataset posted below. You should also draw the scatterplot in SPSS. Instructions for this are provided in SPSS Exercise Q1.
Post your scatter plot and analysis output (specifically, the Model Summary, ANOVA, and Coefficients tables) in the canvas window. Finally, interpret your results consistent with a two-tailed significance test.