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.
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.
Compute a logarithmic regression(LnReg) for the data.
The regression is a method of machine learning under subgroup Supervised Learning. The regression helps to get the relation between the dependent and the independent variables.
The regression equation is obtained by using the given data is used to predict or forecast the values of new data. It can also be used for understanding and analyzing the relation between the variables.
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