conduct a simple linear regression in which you test the association between the
ID: 3239072 • Letter: C
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 483.8785Explanation / 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 weakRelated Questions
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