A Researcher Is Analyzing Whether the Rate of Unlawful Breaking

question 20

Essay

A researcher is analyzing whether the rate of unlawful breaking is effected by the percent of poverty, percent male, percent nonwhite, and the percent of individuals between the ages of 15 and 24 residing in the census block. Given the following SPSS output, what would the researcher conclude? State the null and alternative hypotheses, discuss the F-statistic, the R², R² change, the beta coefficients, and which variable significantly affect the dependent variable.
$\begin{array}{|l|l|l|l|l|l|l|l|l|l|}\hline\\\hline \text { Mod } & & \text { R } & \text { Adjust } & \text { Std. Error } & \text { R } & & & &\text { Sig. F }\\&&\text { Squar } & \text { ed R } & \text { of the } & \text { Square } & & & \\\text { el } & \text { S } & \text { e } & \text { Square} & \text { Estimate } & \text { Change } & \text { F Change } & \text { df1 } & \text { df2 } & \text { Change } \\\\\hline 1 & .195^{\mathrm{a}} & .038 & .031 & 1843.30459 & .038 & 5.294 & 2 & 267 & .006 \\2 & 407 \mathrm{~b} & 166 & 153 & 1723.12310 & 128 & 20.272 & 2 & 265 & .000\\\hline\end{array}$ a. Predictors: (Constant), percent nonwhite, percent poverty
b. Predictors: (Constant), percent nonwhite, percent poverty, percent 15 to 24, percent male $\begin{array}{|l|l|l|l|l|l|} \hline \text { Model }& \text {Sum of Squares } & \text { df } & \text { Mean Square }& \text { F }& \text { Sig. } \\\hline 1 \text { Regression } & 35977621.414 & 2 & 17988810.707 &5.294 & .006^{\mathrm{b}} \\\text { Residual } & 907205072.766 & 267 & 3397771.808 \\\text { Total } & 943182694.179 & 269 & \\\hline 2 \text { Regression } & 156357090.146 & 4 & 39089272.537&13.165 & .000^{\mathrm{c}} \\\text { Residual } & 786825604.033 & 265 & 2969153.223 \\\text { Total } & 943182694.179 & 269 & \\\hline\end{array}$ a. Dependent Variable: rateofubev
b. Predictors: (Constant), percent nonwhite, percent poverty
c. Predictors: (Constant), percent nonwhite, percent poverty, percent 15 to 24, percent male $\begin{array}{l} \begin{array}{|l|l|l|l|}\hline &\text { Unstandardized }&&\text { Standardized }\\ &\text { Coefficients }& &\text { Coefficients }\\\hline \text { Model }& \text { B } & \text { Std. Error }&\text { Beta } \\\hline1\text { (Constant) } & 76.230 & 258.075 \\\text { percentpoverty } & 27.276 & 8.606&.239 \\\hline \text { percentnonwhite } & -5.544 & 4.157&-.101 \\\hline 2\text { (Constant) } & -5080.529 & 1006.335 \\\text { percentpoverty } & 21.254 & 8.173 &.186\\\hline \text { percentnonwhite } & 246 & 3.991 &.004 \\\text { percent15to24 } & -39.467 & 17.899&-.126 \\\text { percentmale } & 116.906 & 19.763&.340\\\hline\end{array}\begin{array}{l|l|}\hline\\\\ t & \text { Sig. } \\\hline .295 & .768 \\3.169 & .002 \\\hline-1.334 & .183 \\\hline-5.049 & .000 \\2.601 & .010 \\\hline .062 & .951 \\\hline-2.205 & .028 \\5.916 & .000 \\\hline\end{array}\end{array}$ a. Dependent Variable: rateofubev

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Definitions:

Standard Deviation

A statistical measure of the dispersion or spread of a set of data points or investment returns around their mean.

Expected Return

The predicted amount of profit or loss an investment is expected to generate over a specific time period.

Probability Distribution

A mathematical formulation that presents all potential values and their chances for a random variable within a particular range.

Real Rate of Return

The annual percentage profit earned on an investment, adjusted for changes in the price level due to inflation or deflation.