Question

Incarceration rates vary from state to state. We must remember that correlation is not causation, but we can ask: “What state level factors might be associated with the state incarceration rate?”

1. Before you look at the data below, state appropriate null and research hypotheses concerning the relationship between Incarceration Rate and Median State Income.
   
   Using the data below, calculate:
2. The prediction equation (least squares line)
3. The Coefficient of Determination
4. Pearson's r
5. Predicted Incarceration Rate for Nebraska based on regression analysis using Median State Household Income.
6. Would multiple regression be a useful statistical tool for further analysis of these data? Why or why not? You do not need to do any calculations to answer this section of the question
7. Incarceration Rate and Median Household Income graph below

8. Please show work. Class does not use SPSS or excel for problems. Thank you.

   	Incarceration	Median
   	rate per 100,000	Income
   	U.S. residents ages 18 or older
   	2016	2016
   State
   Alabama	1080	46257
   Arkansas	1050	44334
   Connecticut	530	73433
   Florida	900	50860
   Idaho	910	51807
   Iowa	560	56247
   Louisiana	1270	45146
   Massachusetts	360	75297
   Mississippi	1260	41754
   Nebraska	610	56927
   New Jersey	460	76126
   Oklahoma	1310	49176
   Rhode Island	370	60596
   Tennessee	930	48547
   Vermont	340	57677
   West Virginia	690	43385
   Mean	789.38	54848.06
   SD	342.06	11378.33

Answer 1

Finding the R square ( Coefficient of determination)

Predicted value for Nebraska

y = 2047.752 - 0.023x = 2047.752 - 0.023(56927) = 738.431