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. Q = 110 – 0.2P – 0.6M + 4.2S + 0.05I (42) (0.12) (0.28) (0.70) (0.024) R2 = 0.74 S.E.E. = 12.9 (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.

Answer 1

i] Test statistic t = 0.2 / 0.12 = 1.666

Critical value of t = 2 at 5% los and 60-2=58 df

here, t valaue < t critical value, we accept H0

There is no significant effect of regression coefficient (price per pound of fish) on prediction or regresssion equation.

ii]

Test statistic t = 0.6 / 0.28 = 2.143

Critical value of t = 2 at 5% los and 60-2=58 df

here, t valaue > t critical value, we do not accept H0

There is significant effect of regression coefficient (meal cost at local restarent) on prediction or regresssion equation.

iii]

Test statistic t = 4.2/ 0.70 = 6

Critical value of t = 2 at 5% los and 60-2=58 df

here, t valaue > t critical value, we do not accept H0

There is significant effect of regression coefficient (seasonal variable) on prediction or regresssion equation.

iv]

Test statistic t = 0.05/0.024=2.0833

Critical value of t = 2 at 5% los and 60-2=58 df

here, t valaue > t critical value, we do not accept H0

There is significant effect of regression coefficient (oncome) on prediction or regresssion equation.

v] R2 = 0.74 , R = 0.8602

Critical value of r =0.254

Here R > r critical values, so we reject H0

Thus we conclude that the regression equation is best fit to the given data