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Exam 10: Regression Analysis: Estimating Relationships

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The two primary objectives of regression analysis are to study relationships between variables and to use those relationships to make predictions.

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For the multiple regression model $\bar { Y } = 40 + 15 X _ { 1 } - 10 X _ { 2 } + 5 X _ { 3 }$ ,if $X _ { 2 }$ were to increase by 5 units,holding $X _ { 1 }$ and $X _ { 3 }$ constant,the value of Y would be expected to decrease by 50 units.

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The least squares line is the line that minimizes the sum of the residuals.

A constant elasticity,or multiplicative,model the dependent variable is expressed as a product of explanatory variables raised to powers

We should include an interaction variable in a regression model if we believe that the effect of one explanatory variable $X _ { 1 }$ on the response variable Y depends on the value of another explanatory variable $X _ { 2 }$ .

Regression analysis can be applied equally well to cross-sectional and time series data.

An important condition when interpreting the coefficient for a particular independent variable X in a multiple regression equation is that:

An outlier is an observation that falls outside of the general pattern of the rest of the observations on a scatterplot.

The multiple R for a regression is the correlation between the observed Y values and the fitted Y values.

Correlation is a summary measure that indicates:

An interaction variable is the product of an explanatory variable and the dependent variable.

The percentage of variation ( $R ^ { 2 }$ ) can be interpreted as the fraction (or percent) of variation of the

The R² can only increase when extra explanatory variables are added to a multiple regression model

In a multiple regression problem with two explanatory variables if,the fitted regression equation is $\hat { Y } = 56.6 - 4.5 X _ { 1 } + 0.60 X _ { 2 } \text {, then the estimated value of } Y \text { when } X _ { 1 } = 2 \text { and } X _ { 2 } = 3 \text { is } 49.4$ .

A regression analysis between weight (Y in pounds)and height (X in inches)resulted in the following least squares line: $\hat { y }$ = 140 + 5X.This implies that if the height is increased by 1 inch,the weight is expected to increase on average by 5 pounds.

A regression analysis between sales (in $1000)and advertising (in $)resulted in the following least squares line: $\hat { Y }$ = 32 + 8X.This implies that an increase of $1 in advertising is expected to result in an increase of $40 in sales.

A regression analysis between sales (in $1000)and advertising (in $100)resulted in the following least squares line: $\hat { Y }$ = 84 +7X.This implies that if advertising is $800,then the predicted amount of sales (in dollars)is $140,000.

Correlation is measured on a scale from 0 to 1,where 0 indicates no linear relationship between two variables,and 1 indicates a perfect linear relationship.

If a scatterplot of residuals shows a parabola shape,then a logarithmic transformation may be useful in obtaining a better fit

The covariance is not used as much as the correlation because