SCMT Quiz 13

When using simple linear regression, we would like to use confidence intervals for the ___________ and prediction intervals for the ___________ at a given value of x. Individual y-value, mean y-value slope, mean slope mean y-value, individual y-value y-intercept, mean y-intercept

mean y-value, individual y-value

The ___________ of the simple linear regression model is the value of y when the mean value of x is zero. slope independent variable y-intercept response variable

y-intercept

Which of the following is a violation of one of the major assumptions of the simple regression model? - As the value of x increases, the value of the error term also increases. - The error terms show no pattern. - The error terms are independent of each other. - A histogram of the residuals forms a bell-shaped, symmetrical curve.

As the value of x increases, the value of the error term also increases.

The standard error of the estimate (standard error) is the estimated standard deviation of the distribution of the independent variable (X) for all values of the dependent variable (Y). True False

False

A significant positive correlation between X and Y implies that changes in X cause Y to change. True False

False

In a simple linear regression model, the coefficient of determination not only indicates the strength of the relationship between the independent and dependent variables, but also shows whether the relationship is positive or negative. True False

False

The error term is the difference between an individual value of the dependent variable and the corresponding mean value of the dependent variable. True False

False

The experimental region is the range of the previously observed values of the dependent variable. True False

False

The point estimate of the variance in a regression model is SSE. b1. MSE. b0.

MSE

The simple linear regression (least squares method) minimizes SSyy. SSE. SSxx. the explained variation. total variation.

SSE

In simple regression analysis, r2 is a percentage measure and measures the proportion of the variation explained by the simple linear regression model. True False

True

The residual is the difference between the observed value of the dependent variable and the predicted value of the dependent variable. True False

True

The simple coefficient of determination is the proportion of total variation explained by the regression line. True False

True

In a simple linear regression analysis, the correlation coefficient (r) and the slope (b) ___________ have the same sign. never always sometimes

always

The ____________ assumption requires that all variation around the regression line should be equal at all possible values (levels) of the ___________variable. control variance, dependent control variance, independent constant variance, dependent constant variance, independent

constant variance, independent

The _____________ measures the strength of the linear relationship between the dependent variable and the independent variable. residual Y-intercept correlation coefficient distance value

correlation coefficient

All of the following are assumptions of the error terms in the simple linear regression model except error terms have a constant variance. error terms are dependent on each other. error terms have a mean of zero. errors are normally distributed.

error terms are dependent on each other.

The _____________ is the range of the previously observed values of x. population region coefficient of determination experimental region slope

experimental region

In simple regression analysis, the quantity Σ(y with a hat-y with a line on top)^2 is called the __________ sum of squares. error unexplained explained total

explained

The ___________ the r2 and the __________ the s (standard error), the stronger the relationship between the dependent variable and the independent variable. higher, lower lower, higher lower, lower higher, higher

higher, lower

Any value of the error term in a regression model _____________ any other value of the error term. is dependent on is independent of increases with is exactly the same as

is independent of

For a given data set, value of X, and confidence level, if all the other factors are constant, the confidence interval for the mean value of Y will ___________ be wider than the corresponding prediction interval for the individual value of Y. sometimes always never

never

The least squares regression line minimizes the sum of the squared differences between actual and predicted Y values. squared differences between actual and predicted X values. absolute deviations between actual and predicted Y values. differences between actual and predicted Y values. absolute deviations between actual and predicted X values.

squared differences between actual and predicted Y values.

The _____ distribution is used for testing the significance of the slope term. r t z r2

t

In simple regression analysis, if the correlation coefficient is a positive value, then - the coefficient of determination can be either positive or negative, depending on the value of the slope. - the standard error of estimate can have either a positive or a negative value. - the least squares regression equation could have either a positive or a negative slope. - the slope of the regression line must also be positive. - the y-intercept must also be a positive value.

the slope of the regression line must also be positive.