It Is Possible That the Distance That a City Is $= 87.6 \% \quad$

question 323

Essay

It is possible that the distance that a city is from the ocean could affect its average January
low temperature. Coast gives an approximate distance of each city from the East Coast or
West Coast (whichever is nearer). Including it in the regression yields the following
regression table: Dependent variable is:JanTemp
R squared $= 87.6 \% \quad$ R squared (adjusted) $= 86.9 \%$ $\mathrm { s } = 4.878$ with $55 - 4 = 51$ degrees of freedom
$\begin{array} { l c c c c } \text { Source } & \text { Sum of Squares } & \text { df } & \text { Mean Square } & \text { F-ratio } \\ \text { Regression } 8611.86 & 3 & 2870.62 & 121 \\ \text { Residual } & 1213.67 & 51 & 23.7974 & \end{array}\\$
$\begin{array} { l c l l r } \text { Variable } & \text { Coefficient } & \text { SE(Coeff) } & \text { t-ratio } & \text { P-value } \\ \text { Intercept } & 111.878 & 6.167 & 18.1 & \leq 0.0001 \\ \text { Lat } & - 2.47722 & 0.1307 & - 19.0 & \leq 0.0001 \\ \text { Long } & 0.221997 & 0.0462 & 4.81 & \leq 0.0001 \\ \text { Coast } & - 0.674929 & 0.0901 & - 7.49 & \leq 0.0001 \end{array}$
And here is a scatterplot of the residuals:
$$\text { Write a report on this regression. Interpret the coefficients and } R ^ { 2 } \text {. Are the conditions met? }$$

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