Concur Technologies, Inc., is a large expense-management company located in Redmond, Washington. The Wall Street Journal asked Concur to examine the data from 8.3 million expense reports to provide insights regarding business travel expenses. Their analysis of the data showed that New York was the most expensive city, with an average daily hotel room rate of $198 and an average amount spent on entertainment, including group meals and tickets for shows, sports, and other events, of$172. In comparison, the U.S. averages for these two categories were $89 for the room rate and$99 for entertainment. The following table shows the average daily hotel room rate and the amount spent on entertainment for a random sample of 9 of the 25 most visited U.S. cities (The Wall Street Journal, August 18, 2011).

City	Room Rate ($)	Entertainment ($)
Boston	148	161
Denver	96	105
Nashville	91	101
New Orleans	110	142
Phoenix	90	100
San Diego	102	120
San Francisco	136	167
San Jose	90	140
Tampa	82	98

a. Develop a scatter diagram for these data with the room rate as the independent variable.

b. What does the scatter diagram developed in part (a) indicate about the relationship between the two variables?

c. Develop the least squares estimated regression equation.

d. Provide an interpretation for the slope of the estimated regression equation.

e. The average room rate in Chicago is $\$128$, considerably higher than the U.S. average. Predict the entertainment expense per day for Chicago.

Following is a portion of the computer output for a regression analysis relating y  maintenance expense (dollars per month) to x = usage (hours per week) of a particular brand of computer terminal.

$$\begin{matrix} \text{The regression equation is}\\ Y=6.1092+.8951X\\\\ \text{Predictor} & \text{Coef} & \text{SE Coef} & \text{Coef}\\ \text{Constant} & \text{6.1092} & \text{0.9361}\\ \text{X} & \text{0.8951} & \text{0.1490}\\\\ \text{Analysis} & \text{of} & \text{Variance}\\\\ \text{SOURCE} & \text{DF} & \text{SS} & \text{MS}\\ \text{Regression} & \text{1} & \text{1575.76} & \text{1575.76}\\ \text{Residual Error} & \text{8} & \text{349.14} & \text{43.64}\\ \text{Total} & \text{9} & \text{1924.90}\\ \end{matrix}$$

a. Write the estimated regression equation. b. Use a t test to determine whether monthly maintenance expense is related to usage at the .05 level of significance. c. Use the estimated regression equation to predict monthly maintenance expense for any terminal that is used 25 hours per week.

An important application of regression analysis in accounting is in the estimation of cost. By collecting data on volume and cost and using the least squares method to develop an estimated regression equation relating volume and cost, an accountant can estimate the cost associated with a particular manufacturing volume. Consider the following sample of production volumes and total cost data for a manufacturing operation.

$$\begin{matrix} \text{Production Volume (units)} & \text{Total Cost (\$)}\\ \text{400} & \text{4000}\\ \text{450} & \text{5000}\\ \text{550} & \text{5400}\\ \text{600} & \text{5900}\\ \text{700} & \text{6400}\\ \text{750} & \text{7000}\\ \end{matrix}$$

Use these data to develop an estimated regression equation that could be used to predict the total cost for a given production volume.

Determine if the conditions for calculating a confidence interval for $\mu$ are met in each of the following settings. An airline wants to calculate the mean number of passengers on a daily 10:00 A.M. flight from Philadelphia to San Diego in 2015. They use flight manifests to determine the mean number of passengers for all these flights in 2015.

Use the following data:

$$\begin{matrix} x_i& \text{2} & \text{6} & \text{9} & \text{13} & \text{20}\\ y_i & \text{7} & \text{18} & \text{9} & \text{26} & \text{23}\\ \end{matrix}$$

The estimated regression equation for these data is $\hat { y } = 7.6 + .9 x .$ What percentage of the total sum of squares can be accounted for by the estimated regression equation? What is the value of the sample correlation coefficient?

Develop a 95% confidence interval for the mean amount spent on entertainment for all cities that have a daily room rate of $89.

An important application of regression analysis in accounting is in the estimation of cost. By collecting data on volume and cost and using the least squares method to develop an estimated regression equation relating volume and cost, an accountant can estimate the cost associated with a particular manufacturing volume. Consider the following sample of production volumes and total cost data for a manufacturing operation.

$$\begin{matrix} \text{Production Volume (units)} & \text{Total Cost (\$)}\\ \text{400} & \text{4000}\\ \text{450} & \text{5000}\\ \text{550} & \text{5400}\\ \text{600} & \text{5900}\\ \text{700} & \text{6400}\\ \text{750} & \text{7000}\\ \end{matrix}$$

The company’s production schedule shows 500 units must be produced next month. What is the estimated total cost for this operation?

Given are five observations collected in a regression study on two variables.

$$\begin{matrix} x_i & \text{2} & \text{6} & \text{9} & \text{13} & \text{20}\\ \hline y_i & \text{7} & \text{18} & \text{9} & \text{26} & \text{23}\\ \end{matrix}$$

Develop a scatter diagram for these data.

Following is a portion of the regression output for an application relating maintenance expense (dollars per month) to usage (hours per week) for a particular brand of computer terminal.

| | Coeffieients Standard Error | t Stat | P-value | | :--- | ---: | ---: | ---: | :---: | | Intercept | 6.1092 | 0.9361 | | | Usage | 0.8951 | 0.149 | |

a. Write the estimated regression equation.

b. Use a t test to determine whether monthly maintenance expense is related to usage at the .05 level of significance.

c. Did the estimated regression equation provide a good fit? Explain.

To the Internal Revenue Service, the reasonableness of total itemized deductions depends on the taxpayer’s adjusted gross income. Large deductions, which include charity and medical deductions, are more reasonable for taxpayers with large adjusted gross incomes. If a taxpayer claims larger than average itemized deductions for a given level of income, the chances of an IRS audit are increased. Data (in thousands of dollars) on adjusted gross income and the average or reasonable amount of itemized deductions follow.

$$\begin{matrix} \text{ } & \text{Reasonable Amount of}\\ \text{Adjusted Gross Income (\$1000s)} & \text{Itemized Deductions (\$1000s)}\\ \hline \text{22} & \text{9.6}\\ \text{27} & \text{9.6}\\ \text{32} & \text{10.1}\\ \text{48} & \text{11.1}\\ \text{65} & \text{13.5}\\ \text{85} & \text{17.7}\\ \text{120} & \text{25.5}\\ \end{matrix}$$

Estimate a reasonable level of total itemized deductions for a taxpayer with an adjusted gross income of $52,500. If this taxpayer claimed itemized deductions of$20,400, would the IRS agent’s request for an audit appear justified? Explain.

To the Internal Revenue Service, the reasonableness of total itemized deductions depends on the taxpayer’s adjusted gross income. Large deductions, which include charity and medical deductions, are more reasonable for taxpayers with large adjusted gross incomes. If a taxpayer claims larger than average itemized deductions for a given level of income, the chances of an IRS audit are increased. Data (in thousands of dollars) on adjusted gross income and the average or reasonable amount of itemized deductions follow.

$$\begin{matrix} \text{ } & \text{Reasonable Amount of}\\ \text{Adjusted Gross Income (\$1000s)} & \text{Itemized Deductions (\$1000s)}\\ \hline \text{22} & \text{9.6}\\ \text{27} & \text{9.6}\\ \text{32} & \text{10.1}\\ \text{48} & \text{11.1}\\ \text{65} & \text{13.5}\\ \text{85} & \text{17.7}\\ \text{120} & \text{25.5}\\ \end{matrix}$$

Use the least squares method to develop the estimated regression equation.

Develop a $95\%$ confidence interval estimate of the population mean monthly rent.

A Wall Street Journal subscriber survey asked 46 questions about subscriber characteristics and interests. State whether the following question provides categorical or quantitative data.

What is your age?

Student Survey In a survey of 125 college students, it was found that of three newspapers, the Wall Street Journal, New York Times, and Chicago Tribune: 60 read the Chicago Tribune ..... 40 read the New York Times 15 read the Wall Street Journal .... 25 read the Chicago Tribune and New York Times 8 read the New York Times and Wall Street Journal .... 3 read the Chicago Tribune and Wall Street Journal ....1 read all three (a) How many read none of these papers? (b) How many read only the Chicago Tribune? (c) How many read neither the Chicago Tribune nor the New York Times?