Suppose you want to study the behavior of sales of automobiles over a

Question

Suppose you want to study the behavior of sales of automobiles over a number of years and someone suggests you to try the following models:

$yt=B_{0}+B_{1}\, t$

$yt=\grave{a}_{0}+\grave{a}_{1}\, t+\grave{a}_{2}\, t^{2}$

Where yt = sales at time t and t = time. The first model postulates that sales is a linear function of time, whereas the second model states that it is a quadratic function of time.

(a) Discuss the properties of these two models.

(b) How would you decide which model is appropriate between these two models?

07 Mar 2024

Answer :

Word Count : 788

### (a) Discuss the properties of these two models: #### Linear Model: - Equation: $ y_t = B_0 + B_1 t $ - Type of relationship: This model assumes a linear relationship between sales and time. The variable $ y_t $ changes in a constant proportion to the variable $ t $ (time). - Intercept ($B_0$): The value of sales at $ t = 0 $, representing the baseline sales when no time has passed. - Slope ($B_1$): This indicates the rate of change of sales over time. A positive $ B_1 $ means sales increase over time, while a negative $ B_1 $ means sales decrease. - Simplicity: It’s simpler, requiring fewer parameters to estimate (only two parameters: $ B_0 $ and $ B_1 $). - Assumption: Assumes that the growth (or decline) in sales is constant over time. #### Quadratic Model: - Equation: $ y_t = a_0 + a_1 t + a_2 t^2 $ - _________ ____ _______ _______ ________.
______ __________ __________ _________ ___ ________.
_____ _______ __________ ______ ______ _________ _______ __________ ______ ____.
_________ _____ _______ ________ ________ ________ ________ ______ _________ _________ __________ ________.
__________ ___ _____ __________ _________ _______ ________ __________.
____ ______ _____ __________ ___ __________.
_______ ______ ___ ___ ____ __________ _______ ____ _______ ___ _________ _____.
_____ ________ ___ __________ ___ __________ ____ __________ _________ ____.
__________ ___ ___ __________ _____ ______ ____ _______ ________ _________.
______ ___ _________ _________ ___.
___ ______ ________ __________ _________ ____ _______.
____ _________ ________ ______ ______ ________.
__________ _______ _____ _________ ______ ______.
______ _______ _______ ________ _________ _________ ______ _______ ________ __________ ___.
____ _____ ____ ________ ______ ________ _________ ___ _______ _____ _______.
_________ _____ __________ _________ ____ ______ _____.
____ _______ ___ ___ ______ _________ _________ ______ _____ ______ _____.
__________ _________ _____ _________ _____ ____ ___ _____ _____ _______ _______.
_______ _________ ____ _____ ______ __________ _______ _______.
________ _____ _________ _____ ______ ___ _________ ________.
_______ _____ ____ _______ ______.
_________ _________ ______ ____ ________ __________ __________ ________.
__________ _________ _______ ______ ______ __________ __________ _______ __________ _________.
________ ______ ___ _________ ____ ______.
_______ ________ _______ _________ ________ ___ __________ ________ ________ ________ _________.
___ ___ ___ ___ ___.
___ _____ __________ ___ _________.
____ ______ ____ ______ ____ _____ _____.
___ _______ ________ __________ _____ ____ ___ ____ ____ _________ _________.
__________ _____ ____ __________ _____ _____ ______ ____ ______ _____ __________ __________.
__________ ________ ________ _________ ____ _____ ____ __________ ________.
_______ ______ ______ _____ ___.
____ __________ _______ __________ ____.
______ ____ _____ _____ ______.
_________ _____ __________ _______ _________ _______ ________ ______ ____ _________ ________ _____.
___ _________ ______ __________ _________ _____ _________ _____ _________ ________.
___ ________ ______ _________ ___ _______ ____ __________.
___ _______ _______ _______ _______ ________.
_____ ______ __________ _______ ________ ______ _______ __________ _______.
______ _________ __________ ________ _____ _________ ___ ______ ___.
_______ _________ _________ ________ ____ _________ ___ __________ _____ __________ ______.
___ __________ ______ _________ ________.
________ ______ ___ ____ ______ ________ ___ ______ _______.
___ _____ _________ ___ ________ ______ _______ ____.
______ __________ __________ _____ ___ ________ __________ __________ ______.
_________ ____ ____ _________ ______ ___ _______ ______ ____ ___.
_______ ____ ______ ______ ______.
______ _________ ____ ________ ________ _____ _____ ________.
______ ____ _______ _____ ___ ________ ________ ________ __________.
___ _________ ________ ______ ______.
____ _______ ________ _____ ____ _______ _____ __________ ___ _____.
_________ _____ ___ ___ _____ _____ __________.
__________ _____ _______ __________ _____ ____ __________ ____ _______ ______ _________ ______.
___ ______ _________ _____ ____ ___ _____ ___ ______ ___.
__________ __________ ________ ___ ___ ________.
______ ______ _______ ________ ______ ________.
_________ ______ __________ _______ ___ ____ ________ _____ _____ _______ _______ _____.
____ ___ _______ _____ _______ _______ ______ ________ ____ ___.
_____ ____ ________ _____ ____ ___ ___ ______.
_____ ___ ______ ____ _________ _____ ____.
_______ _____ ______ _____ ___ ______ ____ _____.
__________ _________ _____ _________ ____ _________ ______.
_____ _________ __________ _______ _____ _________ __________ ______ ____.
_____ ______ _______ ____ _____ ____ _______ ________ _______.
____ ___ ___ _________ _____ __________ _____ ___ _____ _______ _________ __________.
_____ _______ _____ __________ _______ _________ __________ ___ __________.
_____ ________ _____ ________ _________.
__________ _______ _______ ______ ________ __________ _______ _________ ______.
___ _________ ________ ______ _____ ___ _______ ________ ___ ______.
___ _______ __________ _____ _______ ______.
_________ _________ _________ _______ _______ ___.
____ _______ ____ ________ ______ ________ _____ ____ ______ _________ _________ ________.
_________ ______ _________ ________ _______ ____.
______ __________ ________ _____ _______ ___ _____.
______ ___ ________ ________ _____ _____.
________ __________ ______ __________ _______.
___ __________ ______ ___ ______ ______ ________ _________.
____ ________.
Get Full Answer on WhatsApp

IGNOU Solved Assignments Assignments Ignou Projects Project Previous Year Solved Exam Papers Notes Notes Sample Question Papers Sample Question Papers

IGNOU NEWS

Assignment Submission Last Date Extended Till 30 June 2026 Click Here★★★IGNOU June 2026 TEE Date Sheet Released Click Here★★★