# Project #36947 - multiple choice 10

Which of the following is NOT one of the basic assumptions that must be satisfied in order to perform inference for regression of y on x?

 There exists a straight line y = a + b x such that for each value of x, the mean µy of the corresponding population of y-values lies on that straight line. The sample size (the number of paired observations (x, y) in the sample data) exceeds 30. For each value of x, the corresponding population of y-values is normally distributed. The standard deviation s of the population of y-values corresponding to a particular value of x is always the same regardless of the specific value of x.

2.  If the assumptions for regression inference are met, then a normal probability plot of the residuals should be

 Clearly curved Roughly linear A group of randomly scattered points Bell shaped

3.  If a test of hypotheses rejects Ho: b= 0 in favor of the alternative hypothesis Ha: b > 0, where b is the population regression slope, then the least-squares regression line

 Is not useful for predicting y given x Can be extrapolated beyond the limits of the x-values covered by the data to predict y at any possible x Is useful for predicting y given x (within the limits of x-values covered by the data) Slopes downward and to the right when plotted on the scatterplot of paired observations (x, y)

4.  Inference for regression on the population regression slope b is based on which of the following distributions?

 The chi-square distribution with n - 1 degrees of freedom The t distribution with n - 2 degrees of freedom The t distribution with n 1 - degrees of freedom The standard normal distribution

5.  In inference for regression, the statistic s represents

 The standard deviation of the x-values in the paired observations (x, y) The estimate of the y-intercept The estimate of the standard deviation s in the regression model The standard deviation of the y-values in the paired observations (x, y)

6.

A random sample of 80 companies from the Forbes 500 list was selected and the relationship between sales (in hundreds of thousands of dollars) and profits (in hundreds of thousands of dollars) was investigated by regression. A least-squares regression line was fit to the data using statistical software, with sales as the explanatory variable and profits as the response variable. Here is the output from the software:

Dependent variable is Profits

R squares = 66.2%

s = 466.2 with 80- 2 = 78 degrees of freedom

Variable    Coefficient   s.e. of Coefficient     P-value

Constant    -176.644          61.16                0.0050

Sales          0.092498        0.0075             <0.0001

Approximately what is the intercept of the least-squares regression line?

 -176.64 0.0925 0.0075 61.16

7.

A random sample of 80 companies from the Forbes 500 list was selected and the relationship between sales (in hundreds of thousands of dollars) and profits (in hundreds of thousands of dollars) was investigated by regression. A least-squares regression line was fit to the data using statistical software, with sales as the explanatory variable and profits as the response variable. Here is the output from the software:

Dependent variable is Profits

R squares = 66.2%

s = 466.2 with 80- 2 = 78 degrees of freedom

Variable    Coefficient   s.e. of Coefficient     P-value

Constant    -176.644          61.16                0.0050

Sales          0.092498        0.0075             <0.0001

Approximately what is the 90% confidence interval for the slope of the least-squares regression line?

 - 0.0925 ± 0.0075 0.0925 ± 0.0075 0.0925 ± 0.012 - 0.0925 ± 0.012

8.

A random sample of 80 companies from the Forbes 500 list was selected and the relationship between sales (in hundreds of thousands of dollars) and profits (in hundreds of thousands of dollars) was investigated by regression. A least-squares regression line was fit to the data using statistical software, with sales as the explanatory variable and profits as the response variable. Here is the output from the software:

Dependent variable is Profits

R squares = 66.2%

s = 466.2 with 80- 2 = 78 degrees of freedom

Variable    Coefficient   s.e. of Coefficient     P-value

Constant    -176.644          61.16                0.0050

Sales          0.092498        0.0075             <0.0001

What is the value of the t statistic for testing whether the slope of the least-squares regression line is 0?

 0.092 0.0075 0.082 12.73

9.

A random sample of 80 companies from the Forbes 500 list was selected and the relationship between sales (in hundreds of thousands of dollars) and profits (in hundreds of thousands of dollars) was investigated by regression. A least-squares regression line was fit to the data using statistical software, with sales as the explanatory variable and profits as the response variable. Here is the output from the software:

Dependent variable is Profits

R squares = 66.2%

s = 466.2 with 80- 2 = 78 degrees of freedom

Variable Coefficient s.e. of Coefficient P-value

Constant -176.644 61.16 0.0050

Sales 0.092498 0.0075 <0.0001

Is there strong evidence (and if so, why) of a straight line relationship between sales and profits?

 It is impossible to say because we are not given the actual value of the correlation. No, because the value of the square of the correlation is relatively small. Yes, because the slope of the least-squares line is positive. Yes, because the P-value for testing if the slope is 0 is quite small.

 Subject Mathematics Due By (Pacific Time) 08/01/2014 09:00 pm
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