Question

You own a company that raises cattle to sell for beef. Your company needs to forecast sales for the next year to purchase raw materials and plan production. You have a pretty good qualitative grasp of the key causal variables that influence sales quantity but lack quantitative estimates of each variable’s impact on sales. So, you collect historical data on monthly per capita beef consumption (dependent variable) and the causal variables you have identified (price of beef and related meats, household income, price). Using regression analysis, you calculate this relationship. For sales quantity, Q, your data represents pounds per capita; for price, P, its the unit price in dollars; income (I) is the average household income in $1000s (e.g., I = 10 implies average income of $10,000). You generate the following regression equation: Q = 1.24 – 0.23 PB + 0.24 PP + 1.18 PC + 0.24 Y (0.34) (-0.14) (0.11) (0.42) (0.09) where the standard errors are in parentheses. PB is the price of beef, PP is the price of pork, PC is the price of chicken, and Y is household income. The R-square value for this regression estimation is 0.83. You should use a critical value of t = 1.96 in the following questions. a. What does the regression equation tell you? Why is it used in economics? b. Are the above regression coefficients significant? Explain. c. Interpret the R-square value of the regression. What does it imply?

Answer 1

a)

The regression equation gives the relationship between the one dependent variable and the other independent variable. The regression equation is used in economics to establish a mathematical representation of the relationship between variables so that we can predict the value of the dependent variable for the given specific values of independent variables.

The estimated regression equation is defined as,

Q = 1.24 – 0.23 PB + 0.24 PP + 1.18 PC + 0.24 Y

which tells the sales of the company increases with the increase in independent variables PP, PC, and Y while the sales of the company decrease with the increase in independent variables PB.

b)

The estimated regression equation is defined as,

Q = 1.24 – 0.23 PB + 0.24 PP + 1.18 PC + 0.24 Y

(0.34) (-0.14) (0.11) (0.42) (0.09)

The t statistic is obtained using the formula,

Independent variable	Slope coefficient	Std Error	t	t-critical
PB	-0.23	-0.14	1.6429	1.96
PP	0.24	0.11	2.1818	1.96
PC	1.18	0.42	2.8095	1.96
Y	0.24	9	0.0267	1.96

Decision rule:

If the t-statistic is greater than the t-critical value, the null hypothesis is rejected which means the independent variable is statistically significant.

Independent variable	t		t-critical
PB	1.6429	<	1.96	Not significant
PP	2.1818	>	1.96	Significant
PC	2.8095	>	1.96	Significant
Y	0.0267	<	1.96	Not significant

c)

The R-square value tells, how well the regression model fits the data values. The R-square value of the model is 0.83 which means, the model explains approximately 83% of the variance of the data value. Based on this evidence we can conclude the model is a good fit.