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The estimates of the slope and intercept are both significant as it can be seen from the Pvalue. The coefficient for cell_subscription is significant at 1% significance level, while the
intercept is significant at 5% significance level.
The estimate of the slope is telling us that an increase in 1 thousand cellphone subscriptions
increases the number of traffic deaths per year by 0.0911447 units.
The coefficient for the intercept estimate instead is telling us that the average number of
traffic deaths per year is 123.9805.
The estimate for the slope does not look much reasonable because it is unlikely that, given
the significance of the estimate, 1000 thousand more cellphone subscriptions lead to a
increase of less than 1 traffic death per year.
The model estimated in (1) is the following one:
𝑛𝑢𝑚𝑏𝑒𝑟𝑜𝑓𝑑𝑒𝑎𝑡ℎ𝑠 = 𝛽0 + 𝛽1 𝑐𝑒𝑙𝑙𝑠𝑢𝑏𝑠𝑐𝑟𝑖𝑝𝑡𝑖𝑜𝑛𝑠 + 𝑒𝑖
The method used is the classic Ordinary Least Squares method.
The OLS tries to minimize the sum of squared errors
𝛽𝑒𝑠𝑡𝑖𝑚𝑎𝑡𝑒𝑑 = 𝑎𝑟𝑔𝑚𝑖𝑛 𝑆(𝛽)
𝑆(𝛽) = ∑ |𝑦𝑖 − ∑ 𝑋𝑖𝑗 𝛽𝑗 |2 = ||𝒚 − 𝑿𝜷||2
The explanatory power of the regression in (1) is given by the R-squared.
The number shown...
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