CH12

Given that the 95% confidence interval for β1 is (-34.5, 26.8) we can say that because the interval contains ___, it is possible that the slope is 0.

0

Which value of R^2 indicates the best fitting regression line?

0.90 0 <= R^2 <= 1

Given the simple linear regression equation ^y = 15+2x, which of the following is the value of the residual at the point (1, 19)?

2

Given that b1 = 2.1, x bar = 10 and y bar = 65.8, b0 = ____.

44.8

Which of the following is a use of the standard error of estimate in regression analysis?

As a goodness of fit measure.

The Excel regression analysis is found in ___.

Data Analysis > Regression

The greater the magnitude of the slope, the stronger the linear relationship. (T/F)

False

Given the following output from a regression analysis: ^y = -54 + 2.3x, R^2 = .75, p-value = .003 for the zero slope test (α = .05), one would conclude

For each unit increase in X, Y increases by 2.3 units, on average. The slope is significantly different from zero. Approximately 75% of the variation in Y is explained by X.

If the trend line equation is ^y= 15 + 5x, which of the following is the correct interpretation of 5?

For every unit increase in X, Y on the average will increase by 5 units.

The coefficient of determination or R^2 is calculated as

SSR / SST

If the trend line equation is ^y = 15 +5x, which of the following is the correct interpretation of 15?

The line crosses the y axis at y = 15

The use of the standard error of regression, se, as a measure of goodness of fit of a model is best expressed by which of the following statements?

The smaller the value, the better the fit.

If we leave off the error term from the population linear model, the left-hand side of the equation is now the expected value of Y for a given x value. (T/F)

True

Regression calculations are typically done on a computer because the calculations can be quite tedious and lengthy. (T/F)

True

The simple regression line will always pass through the point (x bar, y bar). (T/F)

True

The formulas for the slope and intercept estimates in a simple regression equation are:

b0 = y bar - b1(x bar) b1 = [∑i=1n(xi−x)(yi−y)]/[∑i=1n(xi−x)2]

Given that SSxy = 492.45, SSxx = 234.5, b1 = ___

b1 = SSxy / SSxx b1 = 2.1

A measure of relative fit for a simple regression line is called the R^2 or ____.

coefficient of determination

Which of the following is a measure of how well the regression fits the sample data?

coefficient of determination

To fit a regression line in Excel, the independent and dependent variables should be placed in separate

columns

The goal in regression analysis is to

explain variation in the response variable about its mean.

Total variation in Y = Variation in y ___ by X + ____ variation

explained error

In order to fit a regression line on an Excel scatterplot:

from the ribbon: click on Chart Tools > Layout > Trendline highlight the data points on the scatterplot. Right click and choose Add Trendline.

The common approach to fitting a line to the data in a scatterplot is

minimizing the value of the sum of squared residuals.

If the slope parameter, β1 = -5.12, what does this suggest about the nature of the relationship between X and Y?

negative relationship

The simple regression equation assumes that while the error is not observable, it has a ___ distribution with a mean equal to ___.

normal distribution with a mean equal to 0.

The method used to find the line of best fit (minimizing the sum of the squared residuals) is called the ______ or OLS.

ordinary least squares

Given the population linear model y = β0 + β1 x + ε, the term ε represents

random error due to predictor variables other than X that affect Y

se is an estimate for the standard deviation of the

regression errors

Both the standard error of the slope estimate and the standard error of the intercept estimate are calculated using

se

With the population linear model: Y = β0 + β1X + ε, β1 represents the

slope population parameter

If we fail to reject the null hypothesis that the true slope = 0 then we conclude

that the predictor variable X is not associated with the response variable Y.

The test for zero slope will give the same result as the test for zero correlation because

the tcalc value will be the same in both tests

The test for zero correlation yields the exact same t calculation as

the test for zero slope

The total variation in the response variable is denoted SST which means ___.

total sum of squares

The residual, ei, in a simple linear regression model represents which of the following?

yi - ^yi