AMS 315 Lecture Notes - Lecture 14: System Of Linear Equations, Symmetric Matrix, Row And Column Vectors

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plumfish98

24 Mar 2018

School

Stony Brook University

Department

Applied Mathematics and Statistics

Course

AMS 315

Professor

Stephen Finch

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Document Summary

The research context is that two or more independent variables and one dependent variable have been observed for each of n participants. Here, i will discuss two independent variables x i. The mathematics and analysis for more independent variables generalize routinely. The research team then has a spreadsheet with n vectors of observations xx i. As in chapter 11, one of the variables (here y) is the outcome variable or dependent variable. This is the variable hypothesized to be affected by the other variables in scientific research. They may be hypothesized to predict the outcome variable or to cause a change in the outcome variable. The research task is to document the association between independent and dependent variables. As before, a recommended first step is to create the scatterplots of observations, with the vertical axis representing the dependent variable and the horizontal axis representing one of the independent variables.

Related Questions

Need detailed help/answers/advice.1. A picture framer has a piece of wood that measures one inch wide by 50 inches long. She would like to make a picture frame as shown below, and uses all 50 inches of wood she has. Notice that x and y in our sketch below are the outside dimensions of the frame. The picture looks like a rectangle with the measurements 1 inch around all sides and it says that the length of the rectangle is Y and the width is X. A. Write an equation that expresses the required relationship between variables x, y, and the total length of the wood. I got 2(x+y)=50 B. Solve your equation from part (A) for y in terms of x. Got y=25-x C. Write an expression (i.e. a function) that gives the interior area of the frame as a function of its exterior height x. x^2+25x-50?? Confused on everything from here on out. D. Find the values of x that make the interior area of the picture frame equal to zero. Explain why this is the case in the context of the picture frame problem. Draw the frames that correspond to these two extreme conditions. E. Use your function to find the inside dimensions that will make this area a maximum. State also the maximum internal area of the picture frame. The second part of it goes like this: Now the picture framer would like to rework this problem for a piece of wood of arbitrary length L. [In PART I, L was 50 inches. Now L becomes a new variable so that we can generalize what we did in PART I for a piece of wood of any arbitrary length, L] A. Write an equation that expresses the required relationship between variables x, y, and the total length of the wood L. In PART I, you had a linear equation of the form ax+by = 50 where a and b were numbers. Now you will have a slightly more complicated equation involving x, y and L, i.e. your equation will have three variables, x, y, and L in it. B. Solve your equation from part (A) for y in terms of x and L. C. Use your answer to part (B) to write an expression (i.e. a function) that gives the interior area of the frame as a function of its exterior height x, and the wood length L. [The variable y will not appear in this equation] D. Use your function to find the inside dimensions that will make this area a maximum. Now each of your inside dimensions will depend on L, i.e. they will be functions of L.

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AMS 315 Lecture Notes - Lecture 14: System Of Linear Equations, Symmetric Matrix, Row And Column Vectors

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