A manufacturer of cosmetic products, called Cosmetic International, is using a randomized controlled trial (RCT) to estimate the price elasticity of the demand for a new line of facial products, called CI-Face. This elasticity measure shows how much, say, a 1% increase in their prices would affect the demand for CI-Face. They model the demand facing them, Q_x (measured in number of CI-Face item sold online and in-person), as a function of their prices, P_x(measured in dollar price per CI-Face item), and the price of three set of products that are produced by their rivals but are similar to the newly launched set: P₁, P₂, and P_3. Here is the population regression model that they used:

LnQ_x=c+b*LnP_x+a₁*LnP₁+a₂*LnP₂+a₃*LnP₃+u

We have not yet covered the estimation of parameters in multivariate models (i.e., models with more than one independent variable). We will cover that in our next module. In this Comprehension Assessment and the next one, we focus on one parameter at the time. For example, we only focus on parameter b. In the Comprehension Assessments for the next module, we examine all the parameters at the same time.

Also, since the above model is log-linearized, parameter bis the price elasticity of demand for the new facial products, CI-Face. It shows how much, say, a 1% increase in the prices that are charged by Cosmetic International would affect the demand for CI-Face. Also, parameters a₁, a₂, a₃ represent the cross price elasticities. For example, a₁shows how much, say, a 1% increase in the price of the similar products that are produced by their first rival, Europe Cosmtique, would affect the demand facing Cosmetic International.

The table below summarizes the estimation results:

Parameter	Coefficient	SE	95% CIE LowerLimit	95% CIE UpperLimit
c	0.012	0.001	0.010	0.014
b	-0.601	0.150	-0.898	-0.304
a1	0.023	0.097	-0.169	0.215
a2	0.173	0.026	0.122	0.224
a3	0.052	0.019	0.014	0.090

The results suggest that a 1% increase in price of CI-Face products would lower the demand for them by about 0.6%. Also, the confidence interval estimation for parameter bdoes not include zero, suggesting that the effect is statistically different from zero (and hence significant). With than in mind, it is your job to explore the results for the cross price elasticities.

Question 1 1 pts Choose the correct statement: O Only the price of the third rival is of statistical significance for the demand facing Cosmetic International. O Only the price of the first rival is of statistical significance for the demand facing Cosmetic International. Only the prices of the second and the third rivals are of statistical significance for the demand facing Cosmetic International. O Only the prices of the first and the second rivals are of statistical significance for the demand facing Cosmetic International. O Only the prices of the first and the third rivals are of statistical significance for the demand facing Cosmetic International. O Only the price of the second rival is of statistical significance for the demand facing Cosmetic International. O The prices of all the rivals are of statistical significance for the demand facing Cosmetic International.Question 2 1 pts Choose the correct statement: Despite their statistical significance, the prices that are charged by the first rival is of greater economic significance when compared to the prices that are charged by the third rival. Despite their statistical significance, the prices that are charged by the first rival is of greater economic significance when compared to the prices that are charged by the second rival. O Despite their statistical significance, the prices that are charged by the third rival is of greater economic significance when compared to the prices that are charged by the first rival. O Despite their statistical significance, the prices that are charged by the second rival is of greater economic significance when compared to the prices that are charged by the first rival. O Despite their statistical significance, the prices that are charged by the second rival is of greater economic significance when compared to the prices that are charged by the third rival. Despite their statistical significance, the prices that are charged by the third rival is of greater economic significance when compared to the prices that are charged by the second rival