The table below shows the number of state-registered automatic weapons and the m

Question

The table below shows the number of state-registered automatic weapons and the murder rate for se states, z-thousands of automatic weapons, y murders per 100,000 residents veral Northwestern 11.6 13.7 8.1 10.7 6.7 9.7 3.8 7.2 2.8 6.3 2.6 5.9 2.5 6.1 0.7 4.4 Round answers to 4 decimal places. a) Calculate the correlation coefficient. r b) Perform a hypothesis test to see if the correlation is statistically significant. What is the p-value? c) Is the correlation statistically significant at the 0.1 significance level? Select an answer d) Find the regression equation e) How many murders (on average) per 100,000 residents can be expected in a state with 9.3 thousand automatic Preview weapons? Answer ny murders (on average) per 100,000 residents can be expected in a state with 10.3 thousand automatic weapons? Answer-

Explanation / Answer

We use minitab to solve this question.

MTB > Correlation 'x' 'y'.

Correlation: x, y

Pearson correlation of x and y = 0.9994
P-Value = 0.0000

MTB > Regress;
SUBC> Response 'y';
SUBC> Nodefault;
SUBC> Continuous 'x';
SUBC> Terms x;
SUBC> Constant;
SUBC> Unstandardized;
SUBC> Tmethod;
SUBC> Tanova;
SUBC> Tsummary;
SUBC> Tcoefficients;
SUBC> Tequation.

Regression Analysis: y versus x

Analysis of Variance

Source DF Adj SS Adj MS F-Value P-Value
Regression 1 67.0982 67.0982 4923.77 0.000
x 1 67.0982 67.0982 4923.77 0.000
Error 6 0.0818 0.0136
Total 7 67.1800

Model Summary

S R-sq R-sq(adj) R-sq(pred)
0.116737 99.88% 99.86% 99.80%

Coefficients

Term Coef SE Coef T-Value P-Value VIF
Constant 3.8728 0.0719 53.90 0.000
x 0.8510 0.0121 70.17 0.000 1.00

Regression Equation

y = 3.8728 + 0.8510 x

____________________________________________________________________________________________

a)

r = 0.9994

b)

p-value = 0.0000

c)

At the 0.1 significance level p-value =0.0000 < 0.1 therefor correlation is statistically significant.

d)

Regression equation is,

y^ = 3.8728 + 0.8510 * x

e)

At x = 9.3 thousnds,

y^ = 3.8728 + 0.8510 * 9.3 = 11.7821

On an average 11.7821 (12) murders per 100000 residents can be expected.

f)

At x = 10.3 thousnds,

y^ = 3.8728 + 0.8510 * 10.3 = 12.6381

On an average 12.6381 (13) murders per 100000 residents can be expected.

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