A commercial vegetable and fruit grower carefully observes the relationship between the amount of fertilizer used on a certain variety of pumpkin and the revenue made from sales of the resulting pumpkin crop, recorded in the following table Amount of Fertilizer 250 500 750 1000 | 1250| 1500| 1750 2000| (pounds/acre) Revenue earned 96 145 172 185 192 196 198 199 (dollars/acre) The fertilizer costs $0.14 per pound. What would you advise the grower is the most profitable amount of fertilizer to use? Check your advice by answering/calculating the following. • Is cach pound of fertilizer equally effective? Explain. • Graph the data and then estimate the maximum amount of revenue that can be earmed per acre from your graph. Call this estimate c. • Compute a linear regression for the data.

A commercial vegetable and fruit grower carefully observes the relationship between the amount of fertilizer used on a certain variety of pumpkin and the revenue made from sales of the resulting pumpkin crop, recorded in the following table Amount of Fertilizer 250 500 750 1000 | 1250| 1500| 1750 2000| (pounds/acre) Revenue earned 96 145 172 185 192 196 198 199 (dollars/acre) The fertilizer costs $0.14 per pound. What would you advise the grower is the most profitable amount of fertilizer to use? Check your advice by answering/calculating the following. • Is cach pound of fertilizer equally effective? Explain. • Graph the data and then estimate the maximum amount of revenue that can be earmed per acre from your graph. Call this estimate c. • Compute a linear regression for the data.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Concept explainers

Correlation

Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.

Linear Correlation

A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.

Regression Analysis

Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.

Question

A commercial vegetable and fruit grower carefully observes the relationship between the amount of
fertilizer used on a certain variety of pumpkin and the revenue made from sales of the resulting
pumpkin crop, recorded in the following table
Amount of
Fertilizer
|250 500 750 1000 1250 1500 1750 2000
(pounds/acre)
---
Revenue
earned
96 145 172 185 192 196 198
199
(dollars/acre)
The fertilizer costs $0.14 per pound. What would you advise the grower is the most profitable amount
of fertilizer to use? Check your advice by answering/calculating the following.
• Is cach pound of fertilizer equally effective? Explain.
• Graph the data and then estimate the maximum amount of revenue that can be earned per acre
from your graph. Call this estimate c.
• Compute a linear regression for the data.
• Compute a logarithmic regression(LnReg) for the data.
• Use trial and error on your calculator to fit a function of the form r = c(1 – b") where c is
the estimate for the maximum amount of revenue and 0 < b < 1
• Choose the best model for revenue and then write a total cost function for fertilizer. Use graphs
on your calculator to find where cost equals revenue.
• Write a profit function and graph it to advise the grower on the most profitable amount of
fertilizer to use.

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