A commercial vegetable and fruit grower carefully observes the relationship between the per-acre amount of fertilizer used on a certain variety of pumpkin and the extra revenue made from the sales of the resulting pumpkin crop. These observations are recorded in the following table Amount of fertilizer 250 500 750 1000 1250 1500 1750 2000 (pounds/acre) Extra revenue earned 288 435 516 555 576 588 594 597 (dollars/acre) The fertilizer costs 42 cents per pound. What would you advise the grower is 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.
- Is each pound of fertilizer equally effective?
- Estimate the maximum amount of revenue that can be earned per acre by graphing the data.
- Compute a linear regression.
- Compute a logistic regression.
- Use trial and error on your calculator to fit a function of the form r=c(1−bx)r=c(1-bx) where c is the estimate for the maximum amount of revenue and 0<b<10<b<1
- Choose the best model 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.
Trending now
This is a popular solution!
Step by step
Solved in 3 steps with 1 images
