Exam 16: Simple Linear Regression and Correlation

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U V's and Skin Cancer A medical statistician wanted to examine the relationship between the amount of UV's (x) and incidence of skin cancer (y).As an experiment he found the number of skin cancers detected per 100,000 of population and the average daily sunshine in eight states around the country.These data are shown below. U V's and Skin Cancer A medical statistician wanted to examine the relationship between the amount of UV's (x) and incidence of skin cancer (y).As an experiment he found the number of skin cancers detected per 100,000 of population and the average daily sunshine in eight states around the country.These data are shown below.    -{Sales and Experience Narrative} Calculate the Pearson correlation coefficient.Interpret this result. -{Sales and Experience Narrative} Calculate the Pearson correlation coefficient.Interpret this result.

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If the value of the sum of squares for error SSE equals zero, then the coefficient of determination must equal zero.

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Telemarketing Sales and Experience The general manager of a telemarketing company believes that experience is the most important factor in determining the level of success of a telemarketer.To examine this belief she records last month's sales (in $1,000s) and the years of experience of 10 randomly selected telemarketers.These data are listed below. Telemarketing Sales and Experience The general manager of a telemarketing company believes that experience is the most important factor in determining the level of success of a telemarketer.To examine this belief she records last month's sales (in $1,000s) and the years of experience of 10 randomly selected telemarketers.These data are listed below.    -{Telemarketer Sales and Experience Narrative} Use the predicted and actual values of y to calculate the residuals. -{Telemarketer Sales and Experience Narrative} Use the predicted and actual values of y to calculate the residuals.

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U V's and Skin Cancer A medical statistician wanted to examine the relationship between the amount of UV's (x) and incidence of skin cancer (y).As an experiment he found the number of skin cancers detected per 100,000 of population and the average daily sunshine in eight states around the country.These data are shown below. U V's and Skin Cancer A medical statistician wanted to examine the relationship between the amount of UV's (x) and incidence of skin cancer (y).As an experiment he found the number of skin cancers detected per 100,000 of population and the average daily sunshine in eight states around the country.These data are shown below.    -{UV's and Skin Cancer Narrative} Can we conclude at the 1% significance level that there is a linear relationship between sunshine and skin cancer? -{UV's and Skin Cancer Narrative} Can we conclude at the 1% significance level that there is a linear relationship between sunshine and skin cancer?

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In simple linear regression, most often we perform a two-tail test of the population slope β\beta 1 to determine whether there is sufficient evidence to infer that a linear relationship exists.The null hypothesis is stated as:

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Wayne Newton Concert At a recent Wayne Newton concert, a survey was conducted that asked a random sample of 20 people their age and how many concerts they have attended since the first of the year.The following data were collected: Wayne Newton Concert At a recent Wayne Newton concert, a survey was conducted that asked a random sample of 20 people their age and how many concerts they have attended since the first of the year.The following data were collected:    An Excel output follows:   -{Oil Quality and Price Narrative} Predict with 95% confidence the oil price per barrel for an API degree of 35. An Excel output follows: Wayne Newton Concert At a recent Wayne Newton concert, a survey was conducted that asked a random sample of 20 people their age and how many concerts they have attended since the first of the year.The following data were collected:    An Excel output follows:   -{Oil Quality and Price Narrative} Predict with 95% confidence the oil price per barrel for an API degree of 35. -{Oil Quality and Price Narrative} Predict with 95% confidence the oil price per barrel for an API degree of 35.

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The standard error of estimate The standard error of estimate  is a measure of the:is a measure of the:

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A prediction interval is used when we want to predict a one-time occurrence for a particular value of y when the independent variable is a given x value.

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An outlier is an observation that is unusually small or unusually large.

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Which of the following techniques is used to predict the value of one variable on the basis of other variables?

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The value of the sum of squares for regression SSR can never be larger than the value of sum of squares for error SSE.

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The standard error of the estimate is a measure of the:

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In regression analysis, you predict the value of one variable on the basis of one or more other related variables.The variable being predicted is called the ____________________ variable, and the related variables used to make the prediction are called ____________________ variables.

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Telemarketing Sales and Experience The general manager of a telemarketing company believes that experience is the most important factor in determining the level of success of a telemarketer.To examine this belief she records last month's sales (in $1,000s) and the years of experience of 10 randomly selected telemarketers.These data are listed below. Telemarketing Sales and Experience The general manager of a telemarketing company believes that experience is the most important factor in determining the level of success of a telemarketer.To examine this belief she records last month's sales (in $1,000s) and the years of experience of 10 randomly selected telemarketers.These data are listed below.    -{Telemarketer Sales and Experience Narrative} Use the regression equation   to determine the predicted values of y. -{Telemarketer Sales and Experience Narrative} Use the regression equation Telemarketing Sales and Experience The general manager of a telemarketing company believes that experience is the most important factor in determining the level of success of a telemarketer.To examine this belief she records last month's sales (in $1,000s) and the years of experience of 10 randomly selected telemarketers.These data are listed below.    -{Telemarketer Sales and Experience Narrative} Use the regression equation   to determine the predicted values of y. to determine the predicted values of y.

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Given that Given that   and n = 6, the standard error of estimate is: and n = 6, the standard error of estimate is:

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Error terms that are correlated over time are said to be ____________________.

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A regression analysis between weight (y in pounds) and height (x in inches) resulted in the following least squares line: A regression analysis between weight (y in pounds) and height (x in inches) resulted in the following least squares line:   .This implies that if the height is increased by 1 inch, the weight, on average, is expected to: .This implies that if the height is increased by 1 inch, the weight, on average, is expected to:

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A store manager gives a pre-employment examination to new employees.The test is scored from 1 to 100.He has data on their sales at the end of one year measured in dollars.He wants to know if there is any linear relationship between pre-employment examination score and sales.An appropriate test to use is the t-test of the population correlation coefficient.

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U V's and Skin Cancer A medical statistician wanted to examine the relationship between the amount of UV's (x) and incidence of skin cancer (y).As an experiment he found the number of skin cancers detected per 100,000 of population and the average daily sunshine in eight states around the country.These data are shown below. U V's and Skin Cancer A medical statistician wanted to examine the relationship between the amount of UV's (x) and incidence of skin cancer (y).As an experiment he found the number of skin cancers detected per 100,000 of population and the average daily sunshine in eight states around the country.These data are shown below.    -{UV's and Skin Cancer Narrative} Calculate the standard error of estimate, and describe what this statistic tells you about the regression line. -{UV's and Skin Cancer Narrative} Calculate the standard error of estimate, and describe what this statistic tells you about the regression line.

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We can often detect autocorrelation by graphing the residuals against ____________________.

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