b-2. At the 5% significance level, what is the conclusion to the test? multiple choice 2 Do not reject H0we cannot conclude that the poverty rate and the crime rate are linearly related. Reject H0we can conclude that the poverty rate and the crime rate are linearly related. Do not reject H0we can conclude that the poverty rate and the crime rate are linearly related. Reject H0we cannot conclude that the poverty rate and the crime rate are linearly related. c-1. Construct a 95% confidence interval for the slope coefficient of income. (Negative values should be indicated by a minus sign. Round "tα/2,df" value to 3 decimal places, and final answers to 2 decimal places.)
Correlation
Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.
Linear Correlation
A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.
Regression Analysis
Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.
For a sample of 20 New England cities, a sociologist studies the crime rate in each city (crimes per 100,000 residents) as a
| ANOVA | df | SS | MS | F | Significance F |
| Regression | 2 | 3,949.5 | 1,974.8 | 0.28 | 0.756 |
| Residual | 17 | 118,203.96 | 6,953.17 | ||
| Total | 19 | 122,153.4 | |||
| Coefficients | Standard Error |
t Stat | p-value | |
| Intercept | 726.7716 | 120.7822 | 6.017 | 0.000 |
| Poverty | 4.7901 | 6.4031 | 0.7480 | 0.465 |
| Income | -2.8372 | 18.4228 | −0.1540 | 0.879 |
Choose the appropriate hypotheses to test whether the poverty rate and the crime rate are linearly related.
multiple choice 1
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H0: β1 ≥ 0; HA: β1 < 0
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H0: β1 = 0; HA: β1 ≠ 0
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H0: β1 ≤ 0; HA: β1 > 0
b-2. At the 5% significance level, what is the conclusion to the test?
multiple choice 2
- Do not reject H0we cannot conclude that the poverty rate and the crime rate are linearly related.
- Reject H0we can conclude that the poverty rate and the crime rate are linearly related.
- Do not reject H0we can conclude that the poverty rate and the crime rate are linearly related.
- Reject H0we cannot conclude that the poverty rate and the crime rate are linearly related.
c-1. Construct a 95% confidence interval for the slope coefficient of income. (Negative values should be indicated by a minus sign. Round "tα/2,df" value to 3 decimal places, and final answers to 2 decimal places.)
c-2. Using the confidence interval, determine whether income influences the crime rate at the 5% significance level.
multiple choice 3
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Income is significant in explaining the crime rate, since its slope coefficient significantly differs from zero.
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Income is not significant in explaining the crime rate, since its slope coefficient significantly differs from zero.
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Income is not significant in explaining the crime rate, since its slope coefficient does not significantly differ from zero.
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Income is significant in explaining the crime rate, since its slope coefficient does not significantly differ from zero.
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