Exam 14: Simple Linear Regression

In a regression analysis, the variable that is used to predict the dependent variable ______.

As the goodness of fit for the estimated regression equation increases, the _____.

In simple linear regression analysis, which of the following is NOT true?

In regression analysis, if the dependent variable is measured in dollars, the independent variable _____.

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. $\mathbf {Summary~ Output}$ $\mathbf {Regression~ Statistics}$ Multiple R 0.1347 R Square ? Adjusted R Square ? Standard Error 3.3838 Observations ? ​ Regression ? 2.750 ? ? 0.6322 Residual ? ? 11.45 Total 14 ? ​ Intercept 8.6 2.2197 ? 0.0019 x 0.25 0.5101 ? 0.6322 ​

A company has recorded data on the weekly sales for its product (y) and the unit price of the competitor's product (x). The data resulting from a random sample of seven weeks follows. Use Excel to develop a scatter diagram and to compute the least squares estimated regression equation and the coefficient of determination. Week Price Sales 1 0.33 20 2 0.25 14 3 0.44 22 4 0.40 21 5 0.35 16 6 0.39 19 7 0.29 15 ​

Given below are seven observations collected in a regression study on two variables, x (independent variable) and y (dependent variable). Use Excel to a. Compute a $95 \%$ confidence interval for $E ( y )$ when $x = 5$ . b. Compute a $95 \%$ prediction interval for $y$ when $x = 5$ . x y 2 12 3 9 6 8 7 7 8 6 7 5 9 2

Regression analysis was applied between sales (in $1000s) and advertising (in $100s), and the following regression function was obtained. ? $\hat { y }$ = 500 + 4x ? Based on the above estimated regression line, if advertising is $10,000, then the point estimate for sales (in dollars) is _____.

If the coefficient of determination is a positive value, then the regression equation _____.

Which of the following is correct?

A company has recorded data on the weekly sales for its product (y) and the unit price of the competitor's product (x). The data resulting from a random sample of seven weeks follows. Use Excel's Regression tool to construct a residual plot and use it to determine if any model assumptions have been violated. Week Price Sales 1 0.33 20 2 0.25 14 3 0.44 22 4 0.40 21 5 0.35 16 6 0.39 19 7 0.29 15 ​

The difference between the observed value of the dependent variable and the value predicted by using the estimated regression equation is called _____.

Given below are seven observations collected in a regression study on two variables, x (independent variable) and y (dependent variable). Use Excel to develop a scatter diagram and to compute the least squares estimated regression equation. x y 2 12 3 9 6 8 7 7 8 6 7 5 9 2

The equation that describes how the dependent variable (y) is related to the independent variable (x) is called _____.

A data point (observation) that does not fit the trend shown by the remaining data is called a(n) _____.

In a regression analysis, if SSE = 200 and SSR = 300, then the coefficient of determination is _____.

In a regression analysis, if SSE = 500 and SSR = 300, then the coefficient of determination is _____.

If all the points of a scatter diagram lie on the least squares regression line, then the coefficient of determination for these variables based on these data _____.

In regression analysis, which of the following is NOT a required assumption about the error term ε?

In a regression analysis, if r² = 1, then _____.