Pop-up coffee vendors have been popular in the city of Adelaide in 2013. A Pop-up coffee vendor is interested in knowing how temperature (in degrees Celsius) and number of different pastries and biscuits offered to customers, impacts daily hot coffee sales revenue (in $00's).
A random sample of 6 days was taken, with the daily hot coffee sales revenue and the corresponding temperature and number of different pastries and biscuits offered on that day, noted.
Excel output for a multiple linear regression is given below: $$\begin{array} { | c | c | r | }
\hline \text { Coffee sales revenue } & \text { Temperature } & \text { Pastries/biscuits } \
\hline 6.5 & 25 & 7 \
\hline 10 & 17 & 13 \
\hline 5.5 & 30 & 5 \
\hline 4.5 & 35 & 6 \
\hline 3.5 & 40 & 3 \
\hline 28 & 9 & 15 \
\hline
\end{array}$$ \(\begin{array}{|l|r|l|l|l|l|l|}
\hline \text { SUMMARY OUTPUT } & & & & & & \
\hline \text { Regression Statistios } & & & & & & \
\hline \text { Multiple R } & 0.87 & & & & & \
\hline \text { R Square } & 0.75 & & & & & \
\hline \text { Adjusted R Square } & 0.59 & & & & & \
\hline \text { Standard Error } & 5.95 & & & & & \
\hline \text { Observations } & 6.00 & & & & & \\hline \
\hline \text { ANOVA } & & & & & \
\hline & {d f} & SS & M S & F & \text { Significance } F \
\hline \text { Regression } & 2.00 & 322.14 & 161.07 & 4.55 & 0.12 \
\hline \text { Residual } & 3.00 & 106.20 & 35.40 & & \
\hline \text { Total } & 5.00 & 428.33 & & & \\hline \
\hline & \text { Coeffients } & \text { Standard Error } & \text { tStat } & \text { P-value } & {\text { Lower } 95 \%} & {\text { Upper } 95 \%} \
\hline \text { Intercept } & 18.68 & 37.88 & 0.49 & 0.66 & -101.88 & 139.24 \
\hline \text { Temperature } & -0.50 & 0.83 & -0.60 & 0.59 & -3.15 & 2.15 \
\hline \text { Pastries/biscuits } & 0.49 & 2.02 & 0.24 & 0.82 & -5.94 & 6.92 \
\hline
\end{array}\) a. Write down the multiple regression model.
b. Interpret the coefficient of Temperature.
c. Interpret the coefficient of Pastries/biscuits.

Question

Pop-up coffee vendors have been popular in the city of Adelaide in 2013. A Pop-up coffee vendor is interested in knowing how temperature (in degrees Celsius) and number of different pastries and biscuits offered to customers, impacts daily hot coffee sales revenue (in $00's).
A random sample of 6 days was taken, with the daily hot coffee sales revenue and the corresponding temperature and number of different pastries and biscuits offered on that day, noted.
Excel output for a multiple linear regression is given below: $$\begin{array} { | c | c | r | } 
\hline \text { Coffee sales revenue } & \text { Temperature } & \text { Pastries/biscuits } \
\hline 6.5 & 25 & 7 \
\hline 10 & 17 & 13 \
\hline 5.5 & 30 & 5 \
\hline 4.5 & 35 & 6 \
\hline 3.5 & 40 & 3 \
\hline 28 & 9 & 15 \
\hline
\end{array}$$ \(\begin{array}{|l|r|l|l|l|l|l|}
\hline \text { SUMMARY OUTPUT } & & & & & & \
\hline \text { Regression Statistios } & & & & & & \
\hline \text { Multiple R } & 0.87 & & & & & \
\hline \text { R Square } & 0.75 & & & & & \
\hline \text { Adjusted R Square } & 0.59 & & & & & \
\hline \text { Standard Error } & 5.95 & & & & & \
\hline \text { Observations } & 6.00 & & & & & \\hline \
\hline \text { ANOVA } & & & & & \
\hline & {d f} & SS & M S & F & \text { Significance } F \
\hline \text { Regression } & 2.00 & 322.14 & 161.07 & 4.55 & 0.12 \
\hline \text { Residual } & 3.00 & 106.20 & 35.40 & & \
\hline \text { Total } & 5.00 & 428.33 & & & \\hline \
\hline & \text { Coeffients } & \text { Standard Error } & \text { tStat } & \text { P-value } & {\text { Lower } 95 \%} & {\text { Upper } 95 \%} \
\hline \text { Intercept } & 18.68 & 37.88 & 0.49 & 0.66 & -101.88 & 139.24 \
\hline \text { Temperature } & -0.50 & 0.83 & -0.60 & 0.59 & -3.15 & 2.15 \
\hline \text { Pastries/biscuits } & 0.49 & 2.02 & 0.24 & 0.82 & -5.94 & 6.92 \
\hline
\end{array}\) a. Write down the multiple regression model.
b. Interpret the coefficient of Temperature.
c. Interpret the coefficient of Pastries/biscuits.

Quizplus · Accepted Answer

The Answer of Pop-up coffee vendors have been popular in the city of Adelaide in 2013. A Pop-up coffee vendor is interested in knowing how temperature (in degrees Celsius) and number of different pastries and biscuits offered to customers, impacts daily hot coffee sales revenue (in $00's).
A random sample of 6 days was taken, with the daily hot coffee sales revenue and the corresponding temperature and number of different pastries and biscuits offered on that day, noted.
Excel output for a multiple linear regression is given below: $$\begin{array} { | c | c | r | } 
\hline \text { Coffee sales revenue } & \text { Temperature } & \text { Pastries/biscuits } \
\hline 6.5 & 25 & 7 \
\hline 10 & 17 & 13 \
\hline 5.5 & 30 & 5 \
\hline 4.5 & 35 & 6 \
\hline 3.5 & 40 & 3 \
\hline 28 & 9 & 15 \
\hline
\end{array}$$ \(\begin{array}{|l|r|l|l|l|l|l|}
\hline \text { SUMMARY OUTPUT } & & & & & & \
\hline \text { Regression Statistios } & & & & & & \
\hline \text { Multiple R } & 0.87 & & & & & \
\hline \text { R Square } & 0.75 & & & & & \
\hline \text { Adjusted R Square } & 0.59 & & & & & \
\hline \text { Standard Error } & 5.95 & & & & & \
\hline \text { Observations } & 6.00 & & & & & \\hline \
\hline \text { ANOVA } & & & & & \
\hline & {d f} & SS & M S & F & \text { Significance } F \
\hline \text { Regression } & 2.00 & 322.14 & 161.07 & 4.55 & 0.12 \
\hline \text { Residual } & 3.00 & 106.20 & 35.40 & & \
\hline \text { Total } & 5.00 & 428.33 & & & \\hline \
\hline & \text { Coeffients } & \text { Standard Error } & \text { tStat } & \text { P-value } & {\text { Lower } 95 \%} & {\text { Upper } 95 \%} \
\hline \text { Intercept } & 18.68 & 37.88 & 0.49 & 0.66 & -101.88 & 139.24 \
\hline \text { Temperature } & -0.50 & 0.83 & -0.60 & 0.59 & -3.15 & 2.15 \
\hline \text { Pastries/biscuits } & 0.49 & 2.02 & 0.24 & 0.82 & -5.94 & 6.92 \
\hline
\end{array}\) a. Write down the multiple regression model.
b. Interpret the coefficient of Temperature.
c. Interpret the coefficient of Pastries/biscuits.

Pop-Up Coffee Vendors Have Been Popular in the City of Adelaide