Exam 16: Simple Linear Regression and Correlation

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} Interpret the value of the slope of the regression line.

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.

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 coefficient of determination and discuss what its value tells you about the two variables.

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} Draw a scatter diagram of the data.Comment on whether it appears that a linear model might be appropriate.

Game 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 Winnings & Education Narrative} Use the regression equation to determine the predicted values of y.

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} Determine the coefficient of determination and discuss what its value tells you about the two variables.

Sunshine and Melanoma A medical researcher wanted to examine the relationship between the amount of sunshine (x) in hours, and incidence of melanoma, a type of skin cancer (y).As an experiment he found the number of melanoma cases detected per 100,000 of population and the average daily sunshine in eight counties around the country.These data are shown below. -{Sunshine and Melanoma Narrative} Estimate the number of skin cancer cases per 100,000 people who live in a state that gets 6 hours of sunshine on average.

When the actual values y of a dependent variable and the corresponding predicted values are the same, the standard error of estimate will be 0.0.

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.

The prediction interval for a particular value of y is always wider than the confidence interval for mean value of y, given the same data set, x value, and confidence level.

The spread in the residuals should increase as the predicted value of y increases.

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?

Marc Anthony Concert At a recent Marc Anthony 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: -{Marc Anthony Concert Narrative} Draw a histogram of the residuals.

In a simple linear regression problem, the following statistics are calculated from a sample of 10 observations: .The least squares estimates of the slope and y-intercept are, respectively,

If the coefficient of determination is 0.95, this means that 95% of the y values were predicted correctly by the regression line.

In simple linear regression, the denominator of the standard error of estimate is .

The residual r_i is defined as the difference between the actual value y_i and the estimated value .

SSE stands for ____________________ of squares for ____________________.

The following 10 observations of variables x and y were collected. Find the least squares regression line, and the estimated value of y when x = 3.

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} Conduct a test of the population coefficient of correlation to determine at the 5% significance level whether more experience is related to higher sales, as the manager speculates.