STAT 311 (3 CREDITS) VARIANCE AND REGRESSION ANALYSIS ELECTIVE: ALL STUDENTS. CONTENT Introduction to Computer application of variance and regression analysis. Analysis of Variance: one way classification, tests of additivity Random experiments, experiments with one factor, completely randomized designs, randomized block designs, Latin squares designs Two way classification: random and mixed models, expectations of mean squares, test of additivity, model checking Multiple comparison procedures Experiments with more than two factors, fixed random and mixed models Factorial designs, 2 k factorial experiments Confounding and fractional replication Split-plot and nested designs Regression Analysis: least squares method. Multiple regression (2 or more independent variables), stepwise regression. The variances and covariances of regression coefficients, estimation of residuals The variance of estimators Analysis of variance table for regression Test of a general liner hypotheses Lack of fit Regression with dummy variables Nonlinear regression Matrix approach to regression Summary Excel application of variance and regression analyses.
Introduction to Computer Application MS Excel Application. Using a spreadsheet A spreadsheet is a computer program used to manipulate data and carry out calculations, or chains of calculations. The information in a spreadsheet is stored in a rectangular array of cell. The content of each cell can be a number, text or formula. The power of a spreadsheet is that a cell s numeric value can be linked to the content of one cell as the sum of the contents of two other cells. Furthermore, if the value of a cell is changed anywhere in the spreadsheet, all values dependent on it are recalculated and the new values are displayed immediately. The usual mathematical symbols of +, -, *(for x), /(for ) and ^ (for raising to a power). Parentheses are used in the usual fashion as grouping symbols. 2.1.12 Spreadsheets Electronic spreadsheets provide extensive graphing capabilities and their use is widespread. Because Microsoft products are the most widely used software products on a PC, all the examples will be based on the Microsoft spreadsheet for 2007. It is expected that all later versions of excel will support the handling characteristics of earlier versions with only a few minor changes.
Rows and Columns Every electronic spreadsheet consists of a collection of cells arranged in a rectangular array of columns and rows. To enable the identification of individual cells each cell has an address given by the column label followed by a row label. In excel spreadsheet the columns are labeled alphabetically from A onwards and the row are numbered from 1 onwards. So that the address with address H125 is on the H(8 th ) column of the 125 row as shown below. At any time one particular cell boundary is highlighted with a cursor and this cell is called the active cell 2.1.14 Text and number entry Every cell on the spreadsheet is capable of having numbers or text entered into it via the keyboard. Make the cell with the address B10 the active cell and type in the text: Barth and then press Enter Now make cell B15 the active cell and type in the number 12 followed by Enter
2.1.15 Formulas As well as text and numbers, each cell is capable of containing a formula. In an excel spreadsheet every formula begins with the = (equal) sign when it is being entered at the keyboard. Move the cursor to cell B16 and enter at the keyboard: =5*B15 followed by Enter. The * represents multiplication (x) and the formula states that the contents of cell B16 will be five times the contents of cell B15
2.1.16 Clearing entries To clear an entry, point and click at the cell to be cleared. This makes it the active cell. Click the Home menu to reveal a dropdown menu. Select from this menu the option Clear to reveal a further drop-down menu. In this second menu select All and the cell contents are then cleared as indicated below.
Now make sure that all entries on the spreadsheet have been cleared because we want to use spreadsheet to construct a graph. Construction of a Cartesian graph Follow these instructions to plot the graph of y x 2 3 Enter the number 3 in A1 Highlight the cell A1 to A7 by pointing at A1, holding down the mouse button, dragging the pointer to A7 and then releasing the mouse button (all the cells from A2 to A7 turn black to indicate that they have been selected) Select the Fill Series commands from the command Bar as shown below: Now in the series window change the Step value to 1 and click OK button as depicted below.
Cell A2 to A7 fill with single place decimals ranging from 3 to 3with step value intervals of 1. These are the x values, where 3 x 3 is the x intervals as shown below. In cell B1, type in the formula =A1^2-3 and then press Enter. The number 6 appears in cell B1 that is (9-3 = 6) where -3 is the content of A1. Activate cell B2 and select the Edit-Copy commands Highlight cells B2 to B7 and select Edit-Paste commands Cells B2 to B7 fill with numbers, each being the number in the adjoining cell minus 3. You have just copied the formula in B1into the cells B2 to B7. These are the corresponding y values
Now highlight the two columns of numbers cell A1: B7 Click the Chart Wizard button from the Insert Menu The Chart Wizard appeared, requesting a choice of chart type: Click XY (Scatter) to reveal a further choice of type of XY Scatter charts. Click the type in the top right-hand corner to select it (scatter with data points connected by smooth lines without markers) as indicated below:
y =x^2-3 7 6 5 4 3 2 1 0-4 -3-2 -1 0 1 2 3 4-1 -2-3 -4 Now produce the graphs of the following equations: a. b. y 2 6 x x in the interval 3 3 3 y ( x 2) in the interval 1 5 x step value 0. 5 x step value 0. 3 c. y x 3 6x 2 11x 6 in the interval 1 x 5 step value 0. 3 d. y 2 x 2x e in the interval 1 3 x step value 0. 3
Random numbers
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