Exam 13: Simple Linear Regression Analysis

An experiment was performed on a certain metal to determine if the strength is a function of heating time.Partial results based on a sample of 10 metal sheets are given below.The simple linear regression equation is The time is in minutes,the strength is measured in pounds per square inch,MSE = 0.5, Determine the 95 percent prediction interval for the strength of a metal sheet when the average heating time is 2.5 minutes.

(Short Answer)

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Question 121

Consider the following partial computer output from a simple linear regression analysis. Analysis of Variance Write the equation of the least squares line.

(Short Answer)

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Question 122

The notation Ŷ refers to the average value of the dependent variable Y.

(True/False)

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Question 123

The correlation coefficient is the ratio of explained variation to total variation.

(True/False)

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Question 124

Use the least squares regression equation, and determine the predicted value of y when x = 3.25.

(Short Answer)

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Question 125

An experiment was performed on a certain metal to determine if the strength is a function of heating time.Results based on 10 metal sheets are given below.Use the simple linear regression model. Determine the standard error.

(Short Answer)

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Question 126

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)

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Question 127

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

(True/False)

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Question 128

For the same set of observations on a specified dependent variable,two different independent variables were used to develop two separate simple linear regression models.A portion of the results is presented below. Based on the results given above,we can conclude that:

(Multiple Choice)

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Question 129

A local tire dealer wants to predict the number of tires sold each month.He believes that the number of tires sold is a linear function of the amount of money invested in advertising.He randomly selects 6 months of data consisting of monthly tire sales (in thousands of tires)and monthly advertising expenditures (in thousands of dollars).The simple linear regression equation is ŷ = 3 + 1x.The dealer randomly selects one of the six observations,with a monthly sales value of 8000 tires and monthly advertising expenditures of $7000.Calculate the value of the residual for this observation.

(Short Answer)

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Question 130

In simple regression analysis,the quantity that gives the amount by which Y (dependent variable)changes for a unit change in X (independent variable)is called the:

(Multiple Choice)

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Question 131

Any value of the error term in a regression model _____________ any other value of the error term.

(Multiple Choice)

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Question 132

A local tire dealer wants to predict the number of tires sold each month.He believes that the number of tires sold is a linear function of the amount of money invested in advertising.He randomly selects 6 months of data consisting of tire sales (in thousands of tires)and advertising expenditures (in thousands of dollars).Based on the data set with 6 observations,the simple linear regression model yielded the following results. Calculate the sample correlation coefficient.

(Short Answer)

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Question 133

In a simple regression analysis for a given data set,if the null hypothesis β = 0 is rejected,then the null hypothesis ρ = 0 is also rejected.This statement is ___________ true.

(Multiple Choice)

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Question 134

A local tire dealer wants to predict the number of tires sold each month.He believes that the number of tires sold is a linear function of the amount of money invested in advertising.He randomly selects 6 months of data consisting of tire sales (in thousands of tires)and advertising expenditures (in thousands of dollars).Based on the data set with 6 observations,the simple linear regression equation of the least squares line is ŷ = 3 + 1x. MSE = 4 Using the sums of the squares given above,determine the 95 percent confidence interval for the slope.

(Short Answer)

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Question 135

In simple linear regression analysis,if the error terms exhibit a positive or negative autocorrelation over time,then the assumption of constant variance is violated.

(True/False)

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Question 136

A local tire dealer wants to predict the number of tires sold each month.He believes that the number of tires sold is a linear function of the amount of money invested in advertising.He randomly selects 6 months of data consisting of tire sales (in thousands of tires)and advertising expenditures (in thousands of dollars).Based on the data set with 6 observations,the simple linear regression model yielded the following results. Find the estimated slope.

(Short Answer)

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Question 137

The least squares regression line minimizes the sum of the:

(Multiple Choice)

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Question 138

A data set with 7 observations yielded the following.Use the simple linear regression model. SSE = 1.117 Calculate the coefficient of determination.

(Short Answer)

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Question 139

The point estimate of the variance in a regression model is:

(Multiple Choice)

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Question 140

Showing 121 - 140 of 140

Consider the following partial computer output from a simple linear regression analysis. Analysis of Variance Write the equation of the least squares line.

The notation Ŷ refers to the average value of the dependent variable Y.

The correlation coefficient is the ratio of explained variation to total variation.

Use the least squares regression equation, and determine the predicted value of y when x = 3.25.

An experiment was performed on a certain metal to determine if the strength is a function of heating time.Results based on 10 metal sheets are given below.Use the simple linear regression model. Determine the standard error.

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

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

For the same set of observations on a specified dependent variable,two different independent variables were used to develop two separate simple linear regression models.A portion of the results is presented below. Based on the results given above,we can conclude that:

In simple regression analysis,the quantity that gives the amount by which Y (dependent variable)changes for a unit change in X (independent variable)is called the:

Any value of the error term in a regression model _____________ any other value of the error term.

In a simple regression analysis for a given data set,if the null hypothesis β = 0 is rejected,then the null hypothesis ρ = 0 is also rejected.This statement is ___________ true.

In simple linear regression analysis,if the error terms exhibit a positive or negative autocorrelation over time,then the assumption of constant variance is violated.

The least squares regression line minimizes the sum of the:

A data set with 7 observations yielded the following.Use the simple linear regression model. SSE = 1.117 Calculate the coefficient of determination.

The point estimate of the variance in a regression model is:

An Introduction to Business Statistics

Descriptive Statistics: Tabular and Graphical Methods

Descriptive Statistics: Numerical Methods

Probability

Discrete Random Variables

Continuous Random Variables

Sampling and Sampling Distributions

Confidence Intervals

Hypothesis Testing

Statistical Inferences Based on Two Samples

Experimental Design and Analysis of Variance

Chi-Square Tests

Multiple Regression and Model Building

Process Improvement Using Control Charts

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