Ebook Pearson new international edition (9/E): Part 2
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Ebook Pearson new international edition (9/E): Part 2
www.downloadslide.netMULTIPLE REGRESSIONANALYSISIn simple linear regression, the relationship between a single independent variable and a dependent va Ebook Pearson new international edition (9/E): Part 2ariable is investigated. I he relationship between two variables frequently allows one to accurately predict the dependent variable from knowledge of the independent variable. I Jnlorlunatcly. many real-life forecasting situations are not so simple. More than one independent variable is usually nece Ebook Pearson new international edition (9/E): Part 2ssary in order to predict a dependent variable accurately. Regression models with more than one independent variable are called multiple regression moEbook Pearson new international edition (9/E): Part 2
dels. Most of the concepts introduced in simple linear regression carry over to multiple regression. However.some new concepts arise because more thanwww.downloadslide.netMULTIPLE REGRESSIONANALYSISIn simple linear regression, the relationship between a single independent variable and a dependent va Ebook Pearson new international edition (9/E): Part 2ict a dependent variable.SEVERAL PREDICTOR VARIABLESAs an example, return to the problem in which sales volume of gallons of milk is fore cast from knowledge of price per gallon. Mr. Bump is faced with the problem of making a prediction that is not entirely accurate. He can explain almost 75% of the Ebook Pearson new international edition (9/E): Part 2 differences in gallons of milk sold by using one independent variable. I bus. 25% (I - r2) of the total variation is unexplained. In other words, froEbook Pearson new international edition (9/E): Part 2
m the sample evidence Mr. Bump knows 75% of what he must know to forecast sales volume perfectly, lb do a more accurate job of forecasting, he needs Iwww.downloadslide.netMULTIPLE REGRESSIONANALYSISIn simple linear regression, the relationship between a single independent variable and a dependent va Ebook Pearson new international edition (9/E): Part 2orecast will involve less uncertainly and be more accurate.A search must be conducted for another independent variable that is related Io sales volume of gallons of milk. 1 lowever. this new independent, or predictor, variable cannot relate too highly to the independent variable (price per gallon) a Ebook Pearson new international edition (9/E): Part 2lready in use. If the two independent variables are highly related to each other, they will explain the same variation. and the addition of the secondEbook Pearson new international edition (9/E): Part 2
variable will not improve the forecast.1 In fields such as econometrics and applied statistics, there is a great deal of concern with this problem ofwww.downloadslide.netMULTIPLE REGRESSIONANALYSISIn simple linear regression, the relationship between a single independent variable and a dependent va Ebook Pearson new international edition (9/E): Part 2 same information and therefore do not contribute "new” information about the behavior of lire dependent variable. Ideally, the effects of separate predictor variables on the dependent variable should be unrelated to one another.From Chapter 7 of Husiness Forecasting, Ninth Edition. John E. Hanke. D Ebook Pearson new international edition (9/E): Part 2ean w. Wichern. Copyright £> 2009 by Pearson Education, Inc. All rights reserved.235www.downloadslide.netMultiple Regression AnalysisThe simple solutiEbook Pearson new international edition (9/E): Part 2
on to the problem OÍ two highly related independent variables is merely not to Use both of them together.The multicollinearity problem will be discusswww.downloadslide.netMULTIPLE REGRESSIONANALYSISIn simple linear regression, the relationship between a single independent variable and a dependent va Ebook Pearson new international edition (9/E): Part 2igates the relationships among advertising expense, sales volume. and price per gallon by examining a correlation matrix. Ihe correlation matrix is constructed by computing the simple correlation coefficients (or each combination of pairs of variables.An example of a correlation matrix is illustrate Ebook Pearson new international edition (9/E): Part 2d in I able I.The correlation coefficient that indicates the relationship between variables 1 and 2 is represented as rJ2. Note that the first subscriEbook Pearson new international edition (9/E): Part 2
pt. 1. also refers to the row and the second subscript. 2. also refers to the column in the table. This approach allows one to determine, al a glance,www.downloadslide.netMULTIPLE REGRESSIONANALYSISIn simple linear regression, the relationship between a single independent variable and a dependent va Ebook Pearson new international edition (9/E): Part 2variables 2 and 1: that is. r12 - '21-Therefore, only half of the correlation matrix is necessary. In addition, the correlation of a variable with itself is always 1. so that, for example, ru - 02 - '31 - 1.Mr. Bump runs his data on the computer, and the correlation matrix shown in Table 2 results. Ebook Pearson new international edition (9/E): Part 2An investigation of the relationships among advertising expense, sales volume, and price per gallon indicates that the new independent variable shouldEbook Pearson new international edition (9/E): Part 2
con tribute to improved prediction. The correlation matrix shows that advertising expense has a high positive relationship (rn — ,S9) with the dependwww.downloadslide.netMULTIPLE REGRESSIONANALYSISIn simple linear regression, the relationship between a single independent variable and a dependent va Ebook Pearson new international edition (9/E): Part 2 relationships should permit advertising expenses to explain some of the total variation of sales volume that is not already being explained by price per gallon. As will be seen, when both price per gallon and advertising expense are used to estimate sales volume. A‘- increases to 93.2%.the analysis Ebook Pearson new international edition (9/E): Part 2 of the correlation matrix is an important initial step in the solution of any problem involving multiple independent variables.1 TABLE 1Correlation MEbook Pearson new international edition (9/E): Part 2
atrix 1I aria blnVariables1231'II'1?'132'21'»'233'31'32'331 TABLE 2Correlation Matrix for Mr. Bump’s data 1VariablesVariable*Sain 1Price 2\dverthing 3www.downloadslide.netMULTIPLE REGRESSIONANALYSISIn simple linear regression, the relationship between a single independent variable and a dependent vawww.downloadslide.netMULTIPLE REGRESSIONANALYSISIn simple linear regression, the relationship between a single independent variable and a dependent vaGọi ngay
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