Exam 16: Simple Linear Regression and Correlation

The sample correlation coefficient between x and y is 0.375.It has been found out that the p-value is 0.256 when testing H₀: ρ = 0 against the two-sided alternative H₁: ρ ≠ 0.To test H₀: ρ = 0 against the one-sided alternative H₁: ρ > 0 at a significant level of 0.193,the p-value will be equal to

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: Descriptive Statistics Variable N Mean StDev SE Mean Degrees 13 34.60 4.613 1.280 Price 13 12.730 0.457 0.127 Covariances Degrees Price Degrees 21.281667 Price 2.026750 0.208833 Regression Analysis Predictor Coef StDev T P Constant 9.4349 0.2867 32.91 0.000 Degrees 0.095235 0.008220 11.59 0.000 S = 0.1314 R−Sq = 92.46% R−Sq(adj)= 91.7% Analysis of Variance Source DF SS MS F P Regression 1 2.3162 2.3162 134.24 0.000 Residual Error 11 0.1898 0.0173 Total 12 2.5060 -{Oil Quality and Price Narrative} Use the regression equation to determine the predicted values of y.

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.

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

Allman Brothers Concert At a recent Allman Brothers 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: -{Allman Brothers Concert Narrative} Determine the least squares regression line.

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.

SSE stands for ____________________ of squares for ____________________.

Another name for the residual term in a regression equation is random error.

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} Calculate the Pearson correlation coefficient.What sign does it have? Why?

Comedy Shows Revenues A financier whose specialty is investing in comedy shows has observed that,in general,shows with "big-name" stars seem to generate more revenue than those shows whose stars are less well known.To examine his belief he records the gross revenue and the payment (in $ millions)given to the two highest-paid comedians in the show for ten recently staged shows. ​ ​ -{Comedy Shows Revenues Narrative} Use the regression equation to determine the predicted values of y.

If we are interested in determining whether two variables are linearly related,it is necessary to:

If the coefficient of correlation is −0.80,then the percentage of the variation in y that is explained by the variation in x is:

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 Books Narrative} Estimate with 90% confidence the average selling price of all books with 900 pages.

If the plot of the residuals vs.the predicted values resembles a straight line with non-zero slope,then the regression line fits well.

Game Show Winnings & Education An ardent fan of television game shows has observed that,in general,the more educated the contestant,the less money he or she wins.To test her belief she gathers data about the last eight winners of her favorite game show.She records their winnings in dollars and the number of years of education.The results are as follows. ​ ​ -{Game Show Winnings & Education Narrative} Calculate the Pearson correlation coefficient.What sign does it have? Why?

Trivia Games & Education An ardent fan of television game shows has observed that,in general,the more educated the contestant,the less money he or she wins.To test her belief she gathers data about the last eight winners of her favorite game show.She records their winnings in dollars and the number of years of education.The results are as follows. ​ ​ -{Trivia Games & Education Narrative} Determine the least squares regression line.

Game Show Winnings & Education An ardent fan of television game shows has observed that,in general,the more educated the contestant,the less money he or she wins.To test her belief she gathers data about the last eight winners of her favorite game show.She records their winnings in dollars and the number of years of education.The results are as follows. ​ ​ -{Game Show Winnings & Education Narrative} Conduct a test of the population slope to determine at the 5% significance level whether a negative linear relationship exists between years of education and TV game shows' winnings.

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.

The plot of residuals vs.predicted values should show no patterns if the conditions of a regression analysis are met.

Grateful Dead Concert At a recent Grateful Dead 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.It is suspected that older concert goers tend to go to more of his concerts in one year than younger concert goers.The data and analysis are shown below. An Excel output follows: -{Grateful Dead Concert Narrative} Determine the standard error of estimate and describe what this statistic tells you about the model's fit.