Exam 6: Correlation and Linear Regression

Interpret the value of correlation coefficients and squared correlations. -Shown below is a correlation table showing correlation coefficients between stock Price, earnings per share (EPS) and price / earnings (P / E) ratio for a sample of 19 Publicly traded companies. Which of the following statements is false? Correlations: Stock Price, EPS, PE Stock Price EPS EPS 0.875 PE 0.323 -0.111

Write and interpret a linear regression equation. -A small independent organic food store offers a variety of specialty coffees. To Determine whether price has an impact on sales, the managers kept track of how many Pounds of each variety of coffee were sold last month. Based on the data and summary Statistics shown below, the intercept of the estimated regression line that relates the Response variable (monthly sales) to the predictor variable (price per pound) is PRICE PER POUND POUNDS SOLD \ 3.99 75 \ 5.99 60 \ 7.00 65 \ 12.00 45 \ 4.50 80 \ 7.50 70 \ 15.00 25 \ 10.00 35 \ 12.50 40 \ 8.99 50 Mean \ 8.75 54.50 Standard Deviation \ 3.63 18.33 Correlation -

Interpret a linear regression equation and use it to make a prediction. -Data were collected on monthly sales revenues (in $1,000s) and monthly advertising Expenditures ($100s) for a sample of drug stores. The regression line relating revenues (Y) to advertising expenditure (X) is estimated to be yˆ = −48.3 + 9.00x . The correct Interpretation of the slope is that for each additional

The following scatterplot shows monthly sales figures (in units) and number of months of experience on the job for a sample of 19 salespeople. a. Describe the association between monthly sales and level of experience. b. Do these data satisfy the conditions for computing a correlation coefficient? Explain. c. Estimate the correlation.

Write and interpret a linear regression equation. -A small independent organic food store offers a variety of specialty coffees. To Determine whether price has an impact on sales, the managers kept track of how many Pounds of each variety of coffee were sold last month. Based on the data and summary Statistics shown below, the slope of the estimated regression line that relates the response Variable (monthly sales) to the predictor variable (price per pound) is PRICE PER POUND POUNDS SOLD \ 3.99 75 \ 5.99 60 \ 7.00 65 \ 12.00 45 \ 4.50 80 \ 7.50 70 \ 15.00 25 \ 10.00 35 \ 12.50 40 \ 8.99 50 Mean \ 8.75 54.50 Standard Deviation \ 3.63 18.33 Correlation

Use the following to answer questions 5 - 8. A small independent organic food store offers a variety of specialty coffees. To determine whether price has an impact on sales, the managers kept track of how many pounds of each variety of coffee were sold last month. The data, scatterplot and summary statistics are shown below. PRICE PER POUND POUNDS SOLD \ 3.99 75 \ 5.99 60 \ 7.00 65 \ 12.00 45 \ 4.50 80 \ 7.50 70 \ 15.00 25 \ 10.00 35 \ 12.50 40 \ 8.99 50 Mean \ 8.75 54.50 Standard Deviation \ 3.63 18.33 Correlation -0.927 -Comment on whether each of the following conditions for correlation / linear regression is met. a. Quantitative variable condition. b. Linearity condition. c. Outlier condition.

Use the following to answer questions 5 - 8. A small independent organic food store offers a variety of specialty coffees. To determine whether price has an impact on sales, the managers kept track of how many pounds of each variety of coffee were sold last month. The data, scatterplot and summary statistics are shown below. PRICE PER POUND POUNDS SOLD \ 3.99 75 \ 5.99 60 \ 7.00 65 \ 12.00 45 \ 4.50 80 \ 7.50 70 \ 15.00 25 \ 10.00 35 \ 12.50 40 \ 8.99 50 Mean \ 8.75 54.50 Standard Deviation \ 3.63 18.33 Correlation -0.927 -Find the value of R2. Interpret its meaning in this context.

Use the following to answer questions 5 - 8. A small independent organic food store offers a variety of specialty coffees. To determine whether price has an impact on sales, the managers kept track of how many pounds of each variety of coffee were sold last month. The data, scatterplot and summary statistics are shown below. PRICE PER POUND POUNDS SOLD \ 3.99 75 \ 5.99 60 \ 7.00 65 \ 12.00 45 \ 4.50 80 \ 7.50 70 \ 15.00 25 \ 10.00 35 \ 12.50 40 \ 8.99 50 Mean \ 8.75 54.50 Standard Deviation \ 3.63 18.33 Correlation -0.927 -Estimate the linear regression model that relates the response variable (monthly sales) to the predictor variable (price per pound). a. Find the slope of the regression line. b. Find the intercept of the regression line. c. Write the equation of the linear model.

Assign roles to variables. -A supermarket chain gathers data on the amount they spend on promotional material (e)g., coupons, etc.) and sales revenue generated each quarter. The predictor variable is

Analyze scatterplots and correlation coefficients. -A small independent organic food store offers a variety of specialty coffees. To Determine whether price has an impact on sales, the managers kept track of how many Pounds of each variety of coffee were sold last month. Based on the scatterplot, the Linear relationship between number of pounds of coffee sold per week and price is

For each of the following scenarios indicate which is the predictor variable and which is the response variable. a. A supermarket chain gathers data on the amount they spend on promotional material (specials, coupons, etc.) and sales revenue generated each quarter. b. Government-sponsored research investigated the relationship between number of hours individuals spend on the Internet and age. c. A real estate association conducted a study on home prices and economic strength for different regions of the United States.

Interpret the value of correlations coefficients and squared correlations. -Suppose the correlation, r, between two variables x and y is -0.44. What percentage of The variability in y cannot be explained by x?

Shown below is a correlation table showing correlation coefficients between population (in millions), PC adoption, and cell phone adoption for a sample of 16 countries. Correlations: PC Adoption, Cell Phone Adoption, Population (mill) PC Adoption Cell Phone Adoption Cell Phone Adoption 0.671 Population (mill) 0.376 0.016 a. What is the correlation between PC adoption and population? Interpret. b. What is the correlation between cell phone adoption and population? Interpret. c. What is the correlation between PC adoption and cell phone adoption? Interpret.

Use the following to answer questions 5 - 8. A small independent organic food store offers a variety of specialty coffees. To determine whether price has an impact on sales, the managers kept track of how many pounds of each variety of coffee were sold last month. The data, scatterplot and summary statistics are shown below. PRICE PER POUND POUNDS SOLD \ 3.99 75 \ 5.99 60 \ 7.00 65 \ 12.00 45 \ 4.50 80 \ 7.50 70 \ 15.00 25 \ 10.00 35 \ 12.50 40 \ 8.99 50 Mean \ 8.75 54.50 Standard Deviation \ 3.63 18.33 Correlation -0.927 -Using the estimated regression equation, a. Estimate the monthly sales for a variety of coffee that costs $12 per pound. b. What is the residual for this estimate? What does it mean?

For each of the following scenarios indicate which is the predictor variable and which is the response variable. a. A study examined consumption levels of oil and carbon dioxide emissions for a sample of counties. b. Data were collected on job performance rating and hours of training for a sample of employees at a telecommunications repair facility. c. Salary data as well as years of managerial experience were collected for a sample of executives in the high tech industry.

Interpret a linear regression equation and use it to make a prediction. -Data were collected on monthly sales revenues (in $1,000s) and monthly advertising Expenditures ($100s) for a sample of drug stores. The regression line relating revenues (Y) to advertising expenditure (X) is estimated to be yˆ = −48.3 + 9.00x . The predicted Sales revenue for a month in which $1,000 was spent on advertising is