The manufacturer of Beanie Baby dolls used quarterly price data for 2012I - 2020IV (t = 1,...,36)and the regression equation $P _ { t } = a + b t + c _ { 1 } D 1 _ { t } + c _ { 2 } D 2 _ { t } + c _ { 3 } D 3 _ { t }$ to forecast doll prices in the year 2021. $P _ { t }$ is the quarterly price of dolls,and $D 1 _ { t } , D 2 _ { t }$ and $D 3 _ { t }$ are dummy variables for quarters I,II,and III,respectively. The estimated QUARTERLY increase in price is ______,and the estimated ANNUAL increase in price is ______ .

Question

The manufacturer of Beanie Baby dolls used quarterly price data for 2012I - 2020IV (t = 1,...,36)and the regression equation $P _ { t } = a + b t + c _ { 1 } D 1 _ { t } + c _ { 2 } D 2 _ { t } + c _ { 3 } D 3 _ { t }$ to forecast doll prices in the year 2021. $P _ { t }$ is the quarterly price of dolls,and $D 1 _ { t } , D 2 _ { t }$ and $D 3 _ { t }$ are dummy variables for quarters I,II,and III,respectively.  The estimated QUARTERLY increase in price is ______,and the estimated ANNUAL increase in price is ______ .

Quizplus · Accepted Answer

The regression equation given in the question is:

$P _ { t } = a + b t + c _ { 1 } D 1 _ { t } + c _ { 2 } D 2 _ { t } + c _ { 3 } D 3 _ { t }$

From this equation, we can see that the coefficient of the time variable (t) gives us the estimated quarterly increase in price.

Therefore, the estimated QUARTERLY increase in price is given by the coefficient of the time variable (b) which is $0.20.

To find the estimated ANNUAL increase in price, we need to multiply the quarterly increase by 4.

Therefore, the estimated ANNUAL increase in price is $0.20 x 4 = $0.80.

Hence, the answer is D.

The Manufacturer of Beanie Baby Dolls Used Quarterly Price Data Pt=a+bt+c1D1t+c2D2t+c3D3tP _ { t } = a + b t + c _ { 1 } D 1 _ { t } + c _ { 2 } D 2 _ { t } + c _ { 3 } D 3 _ { t }Pt​=a+bt+c1​D1t​+c2​D2t​+c3​D3t​

The Manufacturer of Beanie Baby Dolls Used Quarterly Price Data $P _ { t } = a + b t + c _ { 1 } D 1 _ { t } + c _ { 2 } D 2 _ { t } + c _ { 3 } D 3 _ { t }$