Exam 12: B: linear Regression and Correlation

Sleep Deprivation Narrative A study was conducted to determine the effects of sleep deprivation on people's ability to solve s. The amount of sleep deprivation varied with 8, 12, 16, 20, and 24 hours without sleep. A total of ten subjects participated in the study, two at each sleep deprivation level. After his or her specified sleep deprivation period, each subject was administered a set of simple addition s, and the number of errors was recorded. These results were obtained: -Refer to Sleep Deprivation Narrative. Use a statistical software to construct the ANOVA table for the linear regression.

Young Aspen Trees and Growth Narrative Let x be the number of leaves on a young aspen tree and let y be the growth of the tree (in mm). The data are as follows. -Refer to Young Aspen Trees and Growth Narrative. Use the t-test to test the hypotheses .

Correlation between Shoreline Erosion and Rainfall A scientist is studying the relationship between x = centimetres of annual rainfall and y = centimetres of shoreline erosion. One study reported the following data. Use the following statistical software output to answer the questions below. s = 0.2416 R-sq = 98.8% R-sq(adj) = 98.6% Analysis of Variance -Refer to Correlation between Shoreline Erosion and Rainfall. Interpret the estimated slope of the regression line in the previous question.

Sales and Experience Narrative The general manager of a chain of furniture 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 $1000s) and the years of experience of ten randomly selected salespeople. These data are listed below. -Refer to Sales and Experience Narrative. Determine the standard error of estimate and describe what this statistic tells you about the regression line.

Ice Cream Sales Narrative The manager of an ice cream store is interested in examining the relationship between sales of ice cream (in litres per day) and maximum temperature of the day. The vendor records the following data for a random sample of five days in the summer, where y is number of litres of ice cream sold per day and x is maximum temperature, in degrees Celsius, recorded for the day: The following summary information was computed: -Refer to Ice Cream Sales Narrative. Find the estimated sales of ice cream for a maximum daily temperature of 34°C.

Salary and Years Narrative A company manager is interested in the relationship between x = number of years that an employee has been with the company and y = the employee's annual salary (in thousands of dollars). The following statistical software output is from a regression analysis for predicting y from x for n = 15 data points. s = 0.8081 R-sq = 97.9% R-sq(adj) = 97.8% -Refer to Salary and Years Narrative. Find and interpret the coefficient of determination.

Sunshine and Skin Cancer Narrative A medical statistician wanted to examine the relationship between the amount of sunshine (x) in hours, 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 counties around the country. These data are shown below: -Refer to Sunshine and Skin Cancer Narrative. Estimate the number of skin cancer per 100,000 of population for six hours of sunshine.

Sleep Deprivation Narrative A study was conducted to determine the effects of sleep deprivation on people's ability to solve s. The amount of sleep deprivation varied with 8, 12, 16, 20, and 24 hours without sleep. A total of ten subjects participated in the study, two at each sleep deprivation level. After his or her specified sleep deprivation period, each subject was administered a set of simple addition s, and the number of errors was recorded. These results were obtained: -Refer to Sleep Deprivation Narrative. How do you describe the strength of the relationship between y and x?

Microwave Sales Narrative A microwave oven manufacturer has collected the data shown below on number of units sold (y) in the thousands of dollars and the number of ads (x) placed during the month. -Refer to Microwave Sales Narrative. Determine the least-squares estimates of the regression parameters, and the least-squares regression line.

Extra Help Sessions Narrative A study was conducted to determine the effect of extra help sessions attended on students' ability to avoid mistakes on a 20-question test. The data shown below represent the number of extra help sessions attended (x) and the average number of mistakes (y) recorded. -Refer to Extra Help Sessions Narrative. Use statistical software to construct the ANOVA table for the linear regression.

Forest Age and Tree Diameter Narrative A scientist is studying the relationship between the age of a forest, x, in years and the average diameter of the trees, y, in cm. One study reported the following data. -Let x be the number of vending machines and let y be the time (in hours) it takes to stock them. The data are as follows. Develop a 95% confidence interval for the average value of y when x = 7.

Income and Education Narrative A professor of economics wants to study the relationship between income (y in $1,000s) and education (x in years). A random sample eight individuals is taken and the results are shown below. -Refer to Income and Education Narrative. Predict with 95% confidence the income of an individual with ten years of education.

Extra Help Sessions Narrative A study was conducted to determine the effect of extra help sessions attended on students' ability to avoid mistakes on a 20-question test. The data shown below represent the number of extra help sessions attended (x) and the average number of mistakes (y) recorded. -Refer to Extra Help Sessions Narrative. Use the regression formulas to find the least-squares line for the data.

Income and Education Narrative A professor of economics wants to study the relationship between income (y in $1,000s) and education (x in years). A random sample eight individuals is taken and the results are shown below. -Refer to Income and Education Narrative. Determine the coefficient of determination and discuss what its value tells you about the two variables.

Income and Attractiveness Narrative In order to determine whether good looks translate into heftier paycheques, an economist collected the data shown below on annual income of doctors (y) in thousands of dollars and attractiveness (x) as recorded on a scale from 1 to 5, based on a panel's rating of head-and-shoulder photographs. -Refer to Income and Attractiveness Narrative. Construct a scatterplot and comment on the relationship between income of doctors and attractiveness.

Wind Velocity and Windmills Narrative A scientist is studying the relationship between wind velocity (x in km/h) and DC output of a windmill (y). The following MINITAB output is from a regression analysis for predicting y from x. s = 0.2435 R-sq = 88.3% R-sq(adj) = 87.3% Analysis of Variance -Refer to Wind Velocity and Windmills Narrative. Predict the DC output for a wind velocity of 22 km/h.

Ice Cream Sales Narrative The manager of an ice cream store is interested in examining the relationship between sales of ice cream (in litres per day) and maximum temperature of the day. The vendor records the following data for a random sample of five days in the summer, where y is number of litres of ice cream sold per day and x is maximum temperature, in degrees Celsius, recorded for the day: The following summary information was computed: -Refer to Ice Cream Sales Narrative. Find and interpret the correlation between maximum daily temperature and daily sales of ice cream.

Delivery Time Narrative Let x be the number of pieces of furniture in a delivery truck and y be the time (in hours) it takes the delivery person to deliver all the pieces of furniture. A simple linear regression analysis related x and y where the least-squares estimates of the regression parameters are a = 1.85 and b = 0.55. -Refer to Delivery Time Narrative. Identify and interpret the slope of the equation.

Ice Cream Sales Narrative The manager of an ice cream store is interested in examining the relationship between sales of ice cream (in litres per day) and maximum temperature of the day. The vendor records the following data for a random sample of five days in the summer, where y is number of litres of ice cream sold per day and x is maximum temperature, in degrees Celsius, recorded for the day: The following summary information was computed: -Refer to Ice Cream Sales Narrative. Test at the 0.05 level of significance.

Age of Forest and Diameter of Trees A scientist is studying the relationship between age of a forest, x, in years and the average diameter of the trees, y, in cm. One study reported the following data. -Refer to Age of Forest and Diameter of Trees. Predict the tree diameter of an 83-year-old forest.