Exam 6: Correlation and Linear Regression

Understand the relationship between the correlation and the regression line. -Suppose the correlation, r, between two variables x and y is -0.44. What would you Predict about a y value if the x value is 2 standard deviations above its mean?

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. Correlations: Stock Price, EPS, PE Stock Price EPS 0.875 0.323 -0.111 a. What is the correlation between stock price and EPS? Interpret. b. What is the correlation between stock price and PE? Interpret. c. What is the correlation between EPS and PE? Interpret.

Understand the relationship between the correlation and the regression line. -A company studying the productivity of their employees on a new information system Was interested in determining if the age (X) of data entry operators influenced the number Of completed entries made per hour (Y). The regression equation is yˆ = 14.374 − 0.145x . If sx=14.04 and sy=2.61, then the correlation coefficient between age and productivity is

Use the following to answer questions 5 - 8. To determine whether the cash bonus paid by a company is related to annual pay, data were gathered for 10 account executives at Johnson Financial Group who received cash bonuses in 2007. The data, scatterplot, and summary statistics are shown below. ANNUAL PAY CASH BONUS \ 70609 \ 11225 \ 58487 \ 6238 \ 104561 \ 14194 \ 43922 \ 4188 \ 82613 \ 11863 \ 116250 \ 13671 \ 76751 \ 7758 \ 68513 \ 20760 \ 137000 \ 55000 \ 94469 \ 34368 Mean \ 85318 \ 17927 Standard Deviation \ 28077 \ 15618 Correlation 0.735 - $\text { Find the value of } R ^ { 2 } \text {. Interpret its meaning in this context. }$

Use the following to answer questions 5 - 8. To determine whether the cash bonus paid by a company is related to annual pay, data were gathered for 10 account executives at Johnson Financial Group who received cash bonuses in 2007. The data, scatterplot, and summary statistics are shown below. ANNUAL PAY CASH BONUS \ 70609 \ 11225 \ 58487 \ 6238 \ 104561 \ 14194 \ 43922 \ 4188 \ 82613 \ 11863 \ 116250 \ 13671 \ 76751 \ 7758 \ 68513 \ 20760 \ 137000 \ 55000 \ 94469 \ 34368 Mean \ 85318 \ 17927 Standard Deviation \ 28077 \ 15618 Correlation 0.735 -Estimate the linear regression model that relates the response variable (cash bonus) to the predictor variable (annual pay). a. Find the slope of the regression line. b. Find the intercept of the regression line. c. Write the equation of the linear model.

Analyze residuals. -Based on the following residual plot, which condition / assumption for linear Regression is not satisfied?

Interpret a linear regression equation and use it to make a prediction. -A company studying the productivity of its employees on a new information system Was interested in determining if the age (X) of data entry operators influenced the number Of completed entries made per hour (Y). The regression equation is yˆ = 14.374 − 0.145x . Suppose the actual completed entries per hour for an operator who is 35 years old was 8. The residual is

Analyze scatterplots and correlation coefficients. -The scatterplot shows monthly sales figures (in units) and number of months of Experience for a sample of salespeople. The association between monthly sales and level Of experience can be described as

In commenting on the increase in home foreclosures, a news reporter stated "there appears to be a strong correlation between home foreclosures and job loss of the head of household." Comment on this statement.

Use the following to answer questions 5 - 8. To determine whether the cash bonus paid by a company is related to annual pay, data were gathered for 10 account executives at Johnson Financial Group who received cash bonuses in 2007. The data, scatterplot, and summary statistics are shown below. ANNUAL PAY CASH BONUS \ 70609 \ 11225 \ 58487 \ 6238 \ 104561 \ 14194 \ 43922 \ 4188 \ 82613 \ 11863 \ 116250 \ 13671 \ 76751 \ 7758 \ 68513 \ 20760 \ 137000 \ 55000 \ 94469 \ 34368 Mean \ 85318 \ 17927 Standard Deviation \ 28077 \ 15618 Correlation 0.735 -Using the estimated regression equation, a. Estimate the cash bonus for an executive at Johnson Financial earning $82, 613 a year. b. What is the residual for this estimate? What does it mean?

Analyze scatterplots and correlation coefficients. -A consumer research group examining the relationship between the price of meat (per Pound) and fat content (in grams) gathered data that produced the following scatterplot. If the point in the lower left hand corner (2 grams of fat; $3.00 per pound) is removed, the Correlation would most likely

Analyze scatterplots and correlation coefficients. -The scatterplot shows monthly sales figures (in units) and number of months of Experience for a sample of salespeople. The correlation between monthly sales and level Of experience is most likely

In discussing how its customers use online services, a bank manager noted "there seems to be a strong correlation between the use of the online bill paying feature and gender." Comment on this statement.

Check conditions for correlation and linear regression. -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 shown Below, which of the following statements is true?

Interpret the value of correlation coefficients and squared correlations. -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 summary statistics Shown below, what percent of the variability in the number of pounds of coffee sold per Week can be explained by price? Mean \ 8.75 54.50 Standard Deviation \ 3.63 18.33 Correlation

Assign roles to variables. -A study examined consumption levels of oil and carbon dioxide emissions for Sample of counties. The response variable in this study is

Use the following to answer questions 5 - 8. To determine whether the cash bonus paid by a company is related to annual pay, data were gathered for 10 account executives at Johnson Financial Group who received cash bonuses in 2007. The data, scatterplot, and summary statistics are shown below. ANNUAL PAY CASH BONUS \ 70609 \ 11225 \ 58487 \ 6238 \ 104561 \ 14194 \ 43922 \ 4188 \ 82613 \ 11863 \ 116250 \ 13671 \ 76751 \ 7758 \ 68513 \ 20760 \ 137000 \ 55000 \ 94469 \ 34368 Mean \ 85318 \ 17927 Standard Deviation \ 28077 \ 15618 Correlation 0.735 -Comment on whether each of the following conditions for correlation / linear regression is met. a. Quantitative variable condition. b. Linearity condition. c. Outlier condition

A consumer research group investigating the relationship between the price of meat (per pound) and the fat content (grams) gathered data that produced the following scatterplot. a. Describe the association between the price of meat and fat content. b. Estimate the correlation. c. If the point in the lower left hand corner ($2.00 per pound, 6 grams of fat) is removed,would the correlation become stronger or weaker or remain the same? Explain.

Analyze scatterplots and correlation coefficients. -For the scatterplot shown below, the likely correlation coefficient is

Analyze residuals. -Linear regression was used to describe the trend in world population over time. Below is a plot of the residuals versus predicted values. What does the plot of residuals Suggest?