An exponential model with a quarterly data forecasting equation is

log(
ˆ
Y
i)=2.0886+0.0016Xi−0.0528Q1−0.0389Q2−0.0449Q3

Where Xi represents the coded quarter, Qi is a dummy variable for quarters, Qi=1 if it is ith quarter.

What is the prediction when Xi=27, and it is the fourth quarter?

Question

An exponential model with a quarterly data forecasting equation is

log(
ˆ
Y
i)=2.0886+0.0016Xi−0.0528Q1−0.0389Q2−0.0449Q3

Where Xi represents the coded quarter, Qi is a dummy variable for quarters, Qi=1 if it is ith quarter.

What is the prediction when Xi=27, and it is the fourth quarter?

BlackTom AI · Accepted Answer

First, restate the given forecasting equation in plain terms: the model specifies log-base-10 of the predicted Y, not the natural log, as
log10( Ŷ_i ) = 2.0886 + 0.0016 X_i − 0.0528 Q1 − 0.0389 Q2 − 0.0449 Q3.
We are told Xi = 27 and that it is the fourth quarter. In this setup, Q1, Q2, and Q3 correspond to the first three quarters, and Q4 (the fourth quarter) is the reference category with its own dummy variable not included in the equation. Therefore, for Q4, Q1 = 0, Q2 = 0, Q3 = 0.
Thus, the equation simplifies to log10( Ŷ ) = 2.0886 + 0.0016*(27) when predicting for Q4.
Compute the product: 0.0016 × 27 = 0.0432. Add this to 2.0886: 2.0886 + 0.0432 = 2.1318.
Since the model uses log10, convert back to Ŷ by raising 10 to the power of both sides: Ŷ = 10^(2.1318).
Now evaluate 10^2.1318. 10^2 = 100, and 10^0.1318 ≈ 1.356 (since 10^0.13 is about 1.348 and 10^0.0018 is tiny). Multiplying gives roughly 100 × 1.356 ≈ 135.6. A more precise calculation yields approximately 135.45.
So the predicted value Ŷ is about 135.45, consistent with a base-10 logarithm being used in the model.

If one mistakenly treats the log as natural log, the back-transformation would use e^(2.1318) ≈ 8.4, which is far from the provided answer. The base-10 interpretation reconciles the result with the given numeric target of around 135.45.

An exponential model with a quarterly data forecasting equation is log( ˆ Y i)=2.0886+0.0016Xi−0.0528Q1−0.0389Q2−0.0449Q3 Where Xi represents the coded quarter, Qi is a dummy variable for quarters, Qi=1 if it is ith quarter. What is the prediction when Xi=27, and it is the fourth quarter?

View Explanation

Log in for full answers

Similar Questions

Consider the following estimated regression model [math: ln⁡(yi)^=0.034−0.023xi]\widehat {\ln (y_i)}=0.034-0.023x_i where [math: ln⁡(.)]\ln (.) denotes the natural log. Which of the following is a correct interpretation?[Fill in the blank]

The following data were collected for two related variables x and y. A scatterplot indicates a non-linear association. The data is linearised using a logx transformation and a least squares line is then fitted. The equation of this line isclosest to:

The following data were collected for two related variables x and y. A scatterplot indicates a non-linear association. The data is linearised using a logx transformation and a least squares line is then fitted. The equation of this line isclosest to:

In a consumer society, many adults channel creativity into buying things

Economic stress and unpredictable times have resulted in a booming industry for self-help products

People born without creativity never can develop it

A product has a selling price of $20, a contribution margin ratio of 40% and fixed cost of $120,000. To make a profit of $30,000. The number of units that must be sold is: Type the number without $ and a comma. Eg: 20000

More Practical Tools for Students Powered by AI Study Helper

Homework AI Solver

Stylized AI Paper Writer

Plagiarism Checker Assistant

Citation AI Academic Writing Tool

In-Class Translation Assistant

AI Note Generator

AI Quiz Answers

Past Exam Questions from University Test Bank

Smart Practice Assistant

Adaptive Practice

Making Your Study Simpler