Exam 14: Simple Linear Regression

Part of an Excel output relating x (independent variable) and y (dependent variable) is shown below. Fill in all the blanks marked with a question mark. Summary Output Regression Statistics Multiple R ? R Square 0.5149 Adjusted R Square ? Standard Error 7.3413 Observations 11 ​ ANOVA df SS MS F Significance F Regression ? ? ? ? 0.0129 Residual ? ? ? Total ? 1000.0000 ​ Coefficients Standard Error t Stat P-value Intercept ? 29.4818 3.7946 0.0043 x ? 0.7000 -3.0911 0.0129 ​

A regression analysis between sales (in $1000s) and price (in dollars) resulted in the following equation: ? $\hat { y}$ = 50,000 ? 8x ? The above equation implies that an increase of _____.

Given below are seven observations collected in a regression study on two variables, x (independent variable) and y (dependent variable). Use Excel's Regression tool to construct a residual plot and use it to determine if any model assumptions have been violated. x y 2 12 3 9 6 8 7 7 8 6 7 5 9 2

It is possible for the coefficient of determination to be _____.

In regression and correlation analysis, if SSE and SST are known, then with this information the _____.

The numerical value of the coefficient of determination ______.

If two variables, x and y, have a strong linear relationship, then _____.

If there is a very strong correlation between two variables, then the coefficient of correlation must be _____.

Coyote Cable has been experiencing an increase in cable service subscribers in recent months due to increased advertising and an influx of new residents to the region. The number of subscribers (in 1000s) for the last 16 months is as follows: Month Sales Month Sales Month Sales 1 12.8 7 20.6 12 23.8 2 14.6 8 18.5 13 25.1 3 15.2 9 19.9 14 24.7 4 16.1 10 23.6 15 26.5 5 15.8 11 24.2 16 28.9 ​ Using simple linear regression, forecast the number of subscribers for months 17, 18, 19, and 20.

In regression analysis, the independent variable is typically plotted on the _____.

A regression analysis between demand (y in 1000 units) and price (x in dollars) resulted in the following equation: ? $\hat {y }$ = 9 ? 3x ? The above equation implies that if the price is increased by $1, the demand is expected to _____.

In a regression analysis, if SST = 4500 and SSE = 1575, then the coefficient of determination is _____.

If the coefficient of correlation is .4, the percentage of variation in the dependent variable explained by the estimated regression equation _____.

Data points having high leverage are often _____.

A procedure used for finding the equation of a straight line that provides the best approximation for the relationship between the independent and dependent variables is ______.

If the coefficient of correlation is a positive value, then the slope of the regression line _____.

Larger values of r² imply that the observations are more closely grouped about the _____.

A regression analysis between sales (y in $1000) and advertising (x in dollars) resulted in the following equation: $\hat { y }$ = 50,000 + 6x ? The above equation implies that an increase of _____.

If the coefficient of determination is .81, then the coefficient of correlation _____.

An observation that has a strong effect on the regression results is called a(n) _____.