AEM 201 1st Edition Lecture 24OUTLINE OF PREVIOUS LECTUREI. Tests About a Single Proportion, Normally Distributed (Critical Value Approach)II. Discerning the Null and Alternate HypothesesOUTLINE OF CURRENT LECTUREI. Regression AnalysisII. Ordinary Least Squares Estimate of the Regression LineIII. Using The Ordinary Least Squares Estimate Of The Regression Line To Estimate Values Of TheDependent Variable YREGRESSION ANALYSIS- Dependent Variable: also called the response variable, this phenomena or characteristic we wishto estimate or predict. The dependent variable is usually denoted y- Independent Variable: also called a predictor variable, this is the phenomena used to estimate orpredict the value of the dependent variable. Independent variables are usually denoted x- Functional Relationship: the unique value of the dependent variable (usually denoted y) can be precisely determined given the value of the independent variable (usually denoted x)-this is often referred to as deterministic relationship between x and yo Positive/direct relationshipo Negative/inverse relationshipo No relationship- Slope: change in the value of the dependent variable that corresponds to a one-unit change in the independent variable. Usually denoted B1- Y-Intercept: value of the dependent variable when the independent variable is 0. Denoted B0- Linear Relationship: the slope is constant at all values of the independent variable- A line based on two points will ALWAYS be linear- Solve for y= B0+ B1xo This will find the equation for the line between two points- Statistical Relationship: the relationship(s) between values of the dependent variable and corresponding values of the independent variable(s) is (are) not deterministic. Thus the value of y is estimated given the value of x. the estimated value of the dependent variable is denoted y hat, and the population slope and y-intercept are usually denoted as 1 and 0- Scatter Diagram: graphical simultaneous presentation of the values of two variables on a Cartesian coordinate systemThese notes represent a detailed interpretation of the professor’s lecture. GradeBuddy is best used as a supplement to your own notes, not as a substitute.- Regressional Analysis: statistical methods fo estimating the relationship between the dependent variable and the independent variable. The estimates of 1 and  are usually denoted as b1 and b0- Linear Regression: indicates that the relationship(s) between the dependent variable and the independent variable(s)- Simple Regression: indicates that the relationship is between the dependent variable and a single independent variable. Thus we would have the equation below as our estimate of the value of the dependent variable y when x=xi- Regression Error (Residual): this is the difference between our estimate of the value of the dependent variable y when x=xi ans the actual value of the dependent variable y when x=xi . The residual for the ith observation is usually denoted as ei so that we have- Ordinary Least Squares (OLS): criteria for fitting an estimated regression line to sample data in which the sum of the squared differences between actual and estimated values of the dependent variable are minimizedo We wish to find the regression line that minimizes the squared regression errors we would commit using the line to estimate the values of yORDINARY LEAST SQUARES ESTIMATE OF THE REGRESSION LINE- How do we interpret this model?o If x increases by 1 unit, we estimate that y increases by however many unitso If x is equal to zero, we estimate y will be some number- Sometimes estimates don’t make sense or aren’t realistic- You cant calculate these on excelUSING THE ORDINARY LEAST SQUARES ESTIMATE OF THE REGRESSION LINE TO ESTIMATE VALUES OFTHE DEPENDENT VARIABLE Y- We have no idea what the relationship between the dependent variable and the independent variable is outside the range of values for x in our sample- An attempt to do so is called extrapolation-this is one of the dangers of using regression analysis- KNOW THE VOCAB FOR THE FINAL-will not have to calculate regression for the