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: $$\begin{array} { | c | c | r | }
\hline \text { Coffee sales revenue } & \text { Temperature } & \text { Pastries/biscuits } \
\hline 6.5 & 25 & 7 \
\hline 10 & 17 & 13 \
\hline 5.5 & 30 & 5 \
\hline 4.5 & 35 & 6 \
\hline 3.5 & 40 & 3 \
\hline 28 & 9 & 15 \
\hline
\end{array}$$ \(\begin{array}{|l|r|r|r|r|r|c|}\hline \text { SUMMARV } \
\text { OUTPUT } \
\hline \text { Regression } \
\text { Stotistics } \
\hline \text { Multiple R } & 0.87 \
\hline \text { R Square } & 0.75 \
\hline \begin{array}{l}
\text { Adjusted R } \
\text { Square }
\end{array} & 0.59 \
\hline \text { Standard Error } & 5.95 \
\hline \text { Otservations } & 6.00 \
\hline\
\hline \text { ANOVA }\
\hline & & & & & \text { Significonce } \
& \text { df } & S S & M S & F & F \
\hline \text { Regression } & 2.00 & 322.14 & 161.07 & 4.55 & 0.12 \\hline \text { Residual } & 3.00 & 106.20 & 35.40 \
\hline \text { Total } & 5.00 & 428.33 & \
\hline\
\hline & \text { Coefficients } & {\begin{array}{c}
\text { Standard } \
\text { Error }
\end{array}} & {\text { tStot }} & \text { Pvolue } & \text { Lower 95\% } & \begin{array}{c}
\text { Upper } \
95 \%
\end{array} \
\hline \text { Intercept } & 18.68 & 37.8 & 0.49 & 0.66 & -101.88 & 139.24 \
\hline \text { Temperature } & -0.50 & 0.83 & -0.60 & 0.59 & -3.15 & 2.15 \
\hline \text { Patries/bisouits } & 0.49 & 2.02 & 0.24 & 0.82 & -5.94 & 6.92 \
\hline
\end{array}\) 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: $$\begin{array} { | c | c | r | } 
\hline \text { Coffee sales revenue } & \text { Temperature } & \text { Pastries/biscuits } \
\hline 6.5 & 25 & 7 \
\hline 10 & 17 & 13 \
\hline 5.5 & 30 & 5 \
\hline 4.5 & 35 & 6 \
\hline 3.5 & 40 & 3 \
\hline 28 & 9 & 15 \
\hline
\end{array}$$ \(\begin{array}{|l|r|r|r|r|r|c|}\hline \text { SUMMARV } \
\text { OUTPUT } \
\hline \text { Regression } \
\text { Stotistics } \
\hline \text { Multiple R } & 0.87 \
\hline \text { R Square } & 0.75 \
\hline \begin{array}{l}
\text { Adjusted R } \
\text { Square }
\end{array} & 0.59 \
\hline \text { Standard Error } & 5.95 \
\hline \text { Otservations } & 6.00 \
\hline\
\hline \text { ANOVA }\
\hline & & & & & \text { Significonce } \
& \text { df } & S S & M S & F & F \
\hline \text { Regression } & 2.00 & 322.14 & 161.07 & 4.55 & 0.12 \\hline \text { Residual } & 3.00 & 106.20 & 35.40 \
\hline \text { Total } & 5.00 & 428.33 & \
\hline\
\hline & \text { Coefficients } & {\begin{array}{c}
\text { Standard } \
\text { Error }
\end{array}} & {\text { tStot }} & \text { Pvolue } & \text { Lower 95\% } & \begin{array}{c}
\text { Upper } \
95 \%
\end{array} \
\hline \text { Intercept } & 18.68 & 37.8 & 0.49 & 0.66 & -101.88 & 139.24 \
\hline \text { Temperature } & -0.50 & 0.83 & -0.60 & 0.59 & -3.15 & 2.15 \
\hline \text { Patries/bisouits } & 0.49 & 2.02 & 0.24 & 0.82 & -5.94 & 6.92 \
\hline
\end{array}\) 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: $$\begin{array} { | c | c | r | } 
\hline \text { Coffee sales revenue } & \text { Temperature } & \text { Pastries/biscuits } \
\hline 6.5 & 25 & 7 \
\hline 10 & 17 & 13 \
\hline 5.5 & 30 & 5 \
\hline 4.5 & 35 & 6 \
\hline 3.5 & 40 & 3 \
\hline 28 & 9 & 15 \
\hline
\end{array}$$ \(\begin{array}{|l|r|r|r|r|r|c|}\hline \text { SUMMARV } \
\text { OUTPUT } \
\hline \text { Regression } \
\text { Stotistics } \
\hline \text { Multiple R } & 0.87 \
\hline \text { R Square } & 0.75 \
\hline \begin{array}{l}
\text { Adjusted R } \
\text { Square }
\end{array} & 0.59 \
\hline \text { Standard Error } & 5.95 \
\hline \text { Otservations } & 6.00 \
\hline\
\hline \text { ANOVA }\
\hline & & & & & \text { Significonce } \
& \text { df } & S S & M S & F & F \
\hline \text { Regression } & 2.00 & 322.14 & 161.07 & 4.55 & 0.12 \\hline \text { Residual } & 3.00 & 106.20 & 35.40 \
\hline \text { Total } & 5.00 & 428.33 & \
\hline\
\hline & \text { Coefficients } & {\begin{array}{c}
\text { Standard } \
\text { Error }
\end{array}} & {\text { tStot }} & \text { Pvolue } & \text { Lower 95\% } & \begin{array}{c}
\text { Upper } \
95 \%
\end{array} \
\hline \text { Intercept } & 18.68 & 37.8 & 0.49 & 0.66 & -101.88 & 139.24 \
\hline \text { Temperature } & -0.50 & 0.83 & -0.60 & 0.59 & -3.15 & 2.15 \
\hline \text { Patries/bisouits } & 0.49 & 2.02 & 0.24 & 0.82 & -5.94 & 6.92 \
\hline
\end{array}\) 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