Exam 16: Simple Linear Regression and Correlat

Sales and Experience The general manager of a chain of department stores believes that experience is the most important factor in determining the level of success of a salesperson. To examine this belief she records last month's sales (in $1,000s)and the years of experience of 10 randomly selected salespeople. These data are listed below. {Sales and Experience Narrative} Do the tests of r and b ₁ in the previous two questions provide the same results? Explain.

Cost of Textbooks The editor of a higher education book publisher claims that a large part of the cost of books is the cost of paper. This implies that larger textbooks will cost more money. As an experiment to analyze the claim, a university student visits the bookstore and records the number of pages and the selling price of twelve randomly selected textbooks. These data are listed below. {Cost of Textbooks Narrative} Draw a scatter diagram of the data. Comment on whether it appears that a linear model might be appropriate.

Given the least squares regression line , and a coefficient of determination of 0.81, the coefficient of correlation is:

{Trivia Games & Education Narrative} Interpret the value of the slope of the regression line.

The value of the sum of squares for regression SSR can never be smaller than 1.

If cov( x , y )= 7.5075 and , then the sample slope coefficient is 2.145.

A straight line regression model with only one independent variable is called a(n)____________________-order linear model.

In testing the hypotheses: H ₀: b ₁ = 0 vs. H ₀: b ₁ ¹ 0, the following statistics are available: , , , , and . The value of the test statistic is:

Oil Quality and Price Quality of oil is measured in API gravity degrees--the higher the degrees API, the higher the quality. The table shown below is produced by an expert in the field who believes that there is a relationship between quality and price per barrel. A partial Minitab output follows: {Oil Quality and Price Narrative} Estimate with 95% confidence the average oil price per barrel for an API degree of 35.

Oil Quality and Price Quality of oil is measured in API gravity degrees--the higher the degrees API, the higher the quality. The table shown below is produced by an expert in the field who believes that there is a relationship between quality and price per barrel. A partial Minitab output follows: {Oil Quality and Price Narrative} Estimate with 95% confidence the average oil price per barrel for an API degree of 35.

Oil Quality and Price Quality of oil is measured in API gravity degrees--the higher the degrees API, the higher the quality. The table shown below is produced by an expert in the field who believes that there is a positive relationship between quality and price per barrel. A partial statistical software output follows: {Oil Quality and Price Narrative} Determine the coefficient of determination and discuss what its value tells you about the two variables.

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: {Wayne Newton Concert Narrative} Predict with 95% confidence the number of concerts attended by a 45 years-old individual.

You use a(n)____________________ interval whenever you want to estimate the mean of y when x is a given value.

The objective of a regression model is to analyze the relationship between two variables, x and y , both of which must be based on ____________________ data.

Cost of Books The editor of a major academic book publisher claims that a large part of the cost of books is the cost of paper. This implies that larger books will cost more money. As an experiment to analyze the claim, a university student visits the bookstore and records the number of pages and the selling price of twelve randomly selected books. These data are listed below. {Cost of Books Narrative} Determine the coefficient of determination and discuss what its value tells you.

In simple linear regression, the coefficient of correlation r and the least squares estimate b ₁ of the population slope b ₁:

The method of least squares requires that the sum of the squared deviations between actual y values in the scatter diagram and y values predicted by the regression line be minimized.

If the error variable e is normally distributed, the test statistic for testing H ₀: b ₁ = 0 has a Student t -distribution with n - 2 degrees of freedom.

In order to predict with 80% confidence the expected value of y for a given value of x in a simple linear regression problem, a random sample of 15 observations is taken. Which of the following t -table values listed below would be used?

The following 10 observations of variables x and y were collected. a. Calculate the standard error of estimate. b. Test to determine if there is enough evidence at the 5% significance level to indicate that x and y are negatively linearly related. c. Calculate the coefficient of correlation, and describe what this statistic tells you about the regression line.