Chapter 12 Simple Regression Einföld aðfallsgreining ©

Null Hypothesis Núll tilgáta The analysis of business and economic processes makes extensive use of relationships between variables. Greining á viðskipta- og hagrænum ferlum notar mikið tengsl milli breyta

Correlation Analysis Fylgnigreining correlation coefficient The correlation coefficient is a quantitative measure of the strength of the linear relationship between two variables. Fylgnistuðull er magnlægur mælikvarði á styrk línulegra tengsla milli tveggja breyta.

Correlation Analysis Fylgnigreining The sample correlation coefficient: Úrtaksfylgnistuðull: where: þar sem:

Correlation Analysis Fylgnigreining The null hypothesis of no linear association: Núllkenning um enga línulega fylgni: where the random variable: Þar sem hendingin: follows a Student’s t Distribution with (n-2) degrees of freedom Fylgir t dreifingu með n-2 frígráður

Tests for Zero Population Correlation Próf um núll þýðisfylgni Let r be the sample correlation coefficient, calculated from a random sample of n pairs of observation from a joint normal distribution. The following tests of the null hypothesis have a significance value  : Með marktæknistig  : 1. To test H 0 against the alternative 1. Prófa H 0 gegn valkostinum the decision rule is Ákvörðunarreglan er:

Tests for Zero Population Correlation (continued) 2. To test H 0 against the alternative the decision rule is Ákvörðunarreglan er

Tests for Zero Population Correlation (continued) 3. To test H 0 against the two-sided alternative Próf gegn tvíhliða valkosti the decision rule is Þá er ákvörðunarreglan Here, t n-2,  is the number for which Where the random variable t n-2 follows a Student’s t distribution with (n – 2) degrees of freedom.

Linear Regression Model Aðfallsgreining (Example 10.2)

Linear Regression Model (Figure 10.1)

Linear Regression Model LINEAR REGRESSION POPULATION EQUATION MODEL Where  0 and  1 are the population model coefficients and  is a random error term.

Linear Regression Outcomes Niðurstaða aðfallsgreiningar Linear regression provides two important results: Aðfallsgreining gefur tvær mikilvægar niðurstöður: 1.Predicted values of the dependent or endogenous variable as a function of an independent or exogenous variable. Spágildi fyrir háðu breytuna eða innri stærðina sem fall af ytri eða óháðu breytunni. 2.Estimated marginal change in the endogenous variable that results from a one unit change in the independent or exogenous variable. Mat á áhrifum jaðarbreytingar á háðu breytuna sem er til komin vegna einnar einingar breytingar óháðu breytunnar.