conduct a simple linear regression in which you test the association between the

Question

conduct a simple linear regression in which you test the association between the EV percentage of foreign-born residents in a geographical area and the RV violent crimes per 100,000 people in the population. Paste your output immediately below and answer the four questions that follow:

a) Report and interpret r-squared. Do you consider this to be a strong, moderate or weak association? Explain.

b) Interpret the p-value for the test of independence between percentage of foreign-born residence and violent crime rate.

c) Interpret the value of the 95% confidence interval for the true slope specified above. Explain how this is in agreement with the result of the t-test in part b.

d) Find and interpret the residual standard deviation.

regress crimeratenmaa pctforeignborn Number of obs Source SS df MS 50 F (1, 48 25.22 1 24928.9144 Prob F Model 24928.9144 0.0000 Residual 47445.7531 48 988.4531 squared 0.3444 Adj squared 0.3308 Total 72374 6675 49 1477.03403 Root MSE 31.44 Coef. Std Err [95 Conf Interval] P> It CrimerateInsa. pct foreignborn 6.406218 1.27564 5.02 0.000 8.971.064 3.841372 -Sons 452.3345 15.6886 28.83 0.000 420.7904 483.8785

Explanation / Answer

a) r-squared = 0.34 ,which means 34.44 % of total variation is explained by given model.

here it is 0.344 ,hence it is moderate.

b) p-value = 0.0000 ,very small value

which means null hypothesis is rejected ,

hence there is sufficient evidence that there existsdependence between percentage of foreign-born residence and violent crime rate.

c)  95% confidence interval for the true slope specified above = ( -8.971,-3.841,)

since each value is less than 0 , we can say slope is not equal to 0 , which is same as obtained from p-value.

d) residual standard deviation = 988.0.5 = 31.4324

Standard Error = (Residual MS)0.5

Value of r Strength of relationship -1.0 to -0.5 or 1.0 to 0.5 Strong -0.5 to -0.3 or 0.3 to 0.5 Moderate -0.3 to -0.1 or 0.1 to 0.3 Weak -0.1 to 0.1 None or very weak

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