Question

The data below shows the number of registered guns, per one-hundred residents, and the raw number of gun "accidents" for several major cities in the United States, over a one year period. Registered gun owners (per 100) 10 120 96 42 56 87 56 84 110 36 Number of gun accidents 25 250 285 126 110 216 165 210 280 75 a) Write the equation of the regression line for these values. b) How many gun accidents would you predict would take place in a city that has five guns per 100 residents?

Answer 1

Our objective here, is to fit a regression line to the given data that would help us predict the number gun accidents (Response / Dependent variable) for a given number of five guns per 100 residents (Predictor / Independent variable).

Let X = Registered gun owners (per 100) and Y = Number of gun accidents

(a) Running a Simple Linear regression for the given data, we would get the fitted regression line of the form:

where and denotes the estimated intercept and slope coefficients, obtained using the formula:

and

Substituting the values,

And,

= 2.396

= 174.2 - (2.396) (69.7)

= 7.199

Hence, the fitted regression line is obtained as:

(b) In a city that has five guns per 100 residents, the gun accidents may be predicted to be:

= 19.179

The predicted number of gun accidents that would take place in a city that has five guns per 100 residents is .