The Drag Net Fishing Company (DNF) has hired you as a consultant to analyze the demand by local restaurants for fresh fish. The available data set includes monthly observations collected over the past 5 years on the number of hundreds of pounds of fish purchased by local restaurants per month (Q), the price per pound of fish (P), the average cost of a meal at a local restaurant (M), a seasonal variable (S) that is equal to one during the tourist season and zero otherwise, and average household income (in thousands of dollars) in the area. The results of a regression analysis (with standard errors in parenthesis) are given below.
$$\begin{array} { l }
Q = 110 - 0.2 P - 0.6 M + 4.2 S + 0.05 I \
\text { (42) } ( 0.12 ) \quad ( 0.28 ) \quad ( 0.70 ) \quad ( 0.024 ) \
\end{array}$$ $$\begin{array}{l}
R ^ { 2 } = 0.74\
\text { S.E.E. } = 12.9
\end{array}$$ (i)Evaluate the statistical significance of the equation as a whole and of each of its coefficients.
(ii)The average values of independent variables in the data set that was used to estimate the equation are P = $8, M = $14, and I = $40,000. Calculate a point estimate of the restaurant demand for fish and a 95 percent interval estimate when it is tourist season. Also, calculate a point estimate of the restaurant demand for fish and a 95 percent interval estimate when it is not tourist season.

Question

The Drag Net Fishing Company (DNF) has hired you as a consultant to analyze the demand by local restaurants for fresh fish. The available data set includes monthly observations collected over the past 5 years on the number of hundreds of pounds of fish purchased by local restaurants per month (Q), the price per pound of fish (P), the average cost of a meal at a local restaurant (M), a seasonal variable (S) that is equal to one during the tourist season and zero otherwise, and average household income (in thousands of dollars) in the area. The results of a regression analysis (with standard errors in parenthesis) are given below.
 $$\begin{array} { l } 
Q = 110 - 0.2 P - 0.6 M + 4.2 S + 0.05 I \
\text { (42) } ( 0.12 ) \quad ( 0.28 ) \quad ( 0.70 ) \quad ( 0.024 ) \
\end{array}$$ $$\begin{array}{l}
R ^ { 2 } = 0.74\
\text { S.E.E. } = 12.9
\end{array}$$ (i)Evaluate the statistical significance of the equation as a whole and of each of its coefficients.
(ii)The average values of independent variables in the data set that was used to estimate the equation are P = $8, M = $14, and I = $40,000. Calculate a point estimate of the restaurant demand for fish and a 95 percent interval estimate when it is tourist season. Also, calculate a point estimate of the restaurant demand for fish and a 95 percent interval estimate when it is not tourist season.

Quizplus · Accepted Answer

The Answer of The Drag Net Fishing Company (DNF) has hired you as a consultant to analyze the demand by local restaurants for fresh fish. The available data set includes monthly observations collected over the past 5 years on the number of hundreds of pounds of fish purchased by local restaurants per month (Q), the price per pound of fish (P), the average cost of a meal at a local restaurant (M), a seasonal variable (S) that is equal to one during the tourist season and zero otherwise, and average household income (in thousands of dollars) in the area. The results of a regression analysis (with standard errors in parenthesis) are given below.
 $$\begin{array} { l } 
Q = 110 - 0.2 P - 0.6 M + 4.2 S + 0.05 I \
\text { (42) } ( 0.12 ) \quad ( 0.28 ) \quad ( 0.70 ) \quad ( 0.024 ) \
\end{array}$$ $$\begin{array}{l}
R ^ { 2 } = 0.74\
\text { S.E.E. } = 12.9
\end{array}$$ (i)Evaluate the statistical significance of the equation as a whole and of each of its coefficients.
(ii)The average values of independent variables in the data set that was used to estimate the equation are P = $8, M = $14, and I = $40,000. Calculate a point estimate of the restaurant demand for fish and a 95 percent interval estimate when it is tourist season. Also, calculate a point estimate of the restaurant demand for fish and a 95 percent interval estimate when it is not tourist season.

The Drag Net Fishing Company (DNF) Has Hired You as a Consultant