The Manufacturer of a Light Fixture Believes That the Dollars $\beta$

question 112

Essay

The manufacturer of a light fixture believes that the dollars spent on advertising,the price of the fixture,and the number of retail stores selling the fixture in a particular month,influence the light fixture sales.The manufacturer randomly selects 10 months and collects the following data: The sales are in thousands of units per month,the advertising is given in hundreds of dollars per month,and the price is the unit retail price for the particular month.Using MINITAB the following computer output is obtained.
The regression equation is
Sales = 31.0 + 0.820 Advertising - 0.325 Price + 1.84 Stores
S = 5.465 R - Sq = 96.7% R - Sq(adj)= 95.0%
Analysis of Variance
Based on the multiple regression model given above,the point estimate of the monthly light fixture sales corresponding to second sample data is 49.82 or 49,820 units.This point estimate is calculated based on the assumption that the company spends $4000 on advertising,the price of the fixture is $60 and the fixture is being sold at 3 retail stores.Additional information related to this point estimate is given below.
Test the usefulness of variable "price" in the model using the null hypothesis H₀: $\beta$ ₂ $\le$ 0,at $\alpha$ = 0.05,and state your conclusions.

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Definitions:

Perceptual Constancy

This is the psychological phenomenon where our perception of objects remains unchanged despite variations in their appearance to our eyes, like changes in size, shape, or color.

Feature Detectors

Neurons in the brain that specialize in responding to specific features of an environment or stimulus, such as edges, angles, or movements, contributing to the perception of objects and patterns.

Visual Cortex

The part of the cerebral cortex responsible for processing visual information, located in the occipital lobe.

Human Brain

The central organ of the human nervous system, enabling thoughts, memories, emotions, and physical movements.