Match the terms with the definitions.

a. adjusted gross income

b. dependent

c. exemption

d. filing status

e. gross income

f. itemized deductions

g. standard deduction

h. tax credit

i. taxable income

__ A stated amount you can subtract from adjusted gross income if you do not itemize deductions

The data from exercise mentioned follow.

$x_i$	3	12	6	20	14
$y_i$	55	40	55	10	15

a. Estimate the standard deviation of $\hat{y}^*$ when x=8.

b. Develop a 95% confidence interval for the expected value of y when x=8.

c. Estimate the standard deviation of an individual value of y when x=8.

d. Develop a 95% prediction interval for y when x=8.

Use the following data:

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

Use the $F$ test to test for a significant relationship. Use $\alpha = .05 .$ What is your conclusion?

Business Ethics. Jason Trevor owns a commercial bakery in Blakely, Georgia, that produces a variety of goods sold in grocery stores. Trevor is required by law to perform internal tests on food produced at his plant to check for contamination. On three occasions, the tests of food products containing peanut butter were positive for salmonella contamination. Trevor was not required to report the results to U.S. Food and Drug Administration officials, however, so he did not. Instead, Trevor instructed his employees to simply repeat the tests until the results were negative. Meanwhile, the products that had originally tested positive for salmonella were eventually shipped out to retailers.

Five people who ate Trevor's baked goods that year became seriously ill, and one person died from a salmonella infection. Even though Trevor's conduct was legal, was it unethical for him to sell goods that had once tested positive for salmonella? Why or why not? (See Ethics and the Role of Business.)

Use the following data:

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

Test for a significant relationship by using the $t$ test. Use $\alpha = .05$.

Jason Trevor owns a commercial bakery in Blakely, Georgia, that produces a variety of goods sold in grocery stores. Trevor is required by law to perform internal tests on food produced at his plant to check for contamination. Three times in $2011$, the tests of food products that contained peanut butter were positive for salmonella contamination. Trevor was not required to report the results to U.S. Food and Drug Administration officials, however, so he did not. Instead, Trevor instructed his employees to simply repeat the tests until the outcome was negative. Therefore, the products that had originally tested positive for salmonella were eventually shipped out to retailers. Five people who ate Trevor's baked goods in $2011$ became seriously ill, and one person died from salmonella. Even though Trevor's conduct was legal, was it unethical for him to sell goods that had once tested positive for salmonella? If Trevor had followed the six basic guidelines for making ethical business decisions, would he still have sold the contaminated goods? Why or why not?

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

$\boldsymbol{x}_i$	2	6	9	13	20
$\boldsymbol{y}_i$	7	18	9	26	23

a. Develop a scatter diagram for these data.

b. Develop the estimated regression equation for these data.

c. Use the estimated regression equation to predict the value of y when x=6.

Why is accounting important for financial analysis?

What is regression analysis? Describe the process of performing regression analysis on a graphing utility.

The data is below:

$$\begin{array}{r|rrrrr} x_i & 2 & 6 & 9 & 13 & 20 \\ \hline y_i & 7 & 18 & 9 & 26 & 23 \end{array}$$

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?

A large city hospital conducted a study to investigate the relationship between the number of unauthorized days that employees are absent per year and the distance (miles) between home and work for the employees. A sample of 10 employees was selected and the following data were collected.

$$\begin{array}{cc}\text{Distance to Work} & \text{Number of Days}\\\text { (miles) } & \text { Absent } \\ 1 & 8 \\ 3 & 5 \\ 4 & 8 \\ 6 & 7 \\ 8 & 6 \\ 10 & 3 \\ 12 & 5 \\ 14 & 2 \\ 14 & 4 \\ 18 & 2\end{array}$$

a. Develop a scatter diagram for these data. Does a linear relationship appear reasonable? Explain.

b. Develop the least squares estimated regression equation that relates the distance to work to the number of days absent.

c. Predict the number of days absent for an employee that lives 5 miles from the hospital.

David’s Landscaping has collected data on home values (in thousands of $\$$) and expenditures (in thousands of$\ $$ ) on landscaping with the hope of developing a predictive model to help marketing to potential new clients. Data for $14$ households may be found in the file Landscape.\ a. Develop a scatter diagram with home value as the independent variable.\ b. What does the scatter plot developed in part (a) indicate about the relationship between the two variables?\ c. Use the least squares method to develop the estimated regression equation.\ d. For every additional $\$1000$ in home value, estimate how much additional will be spent on landscaping.\ e. Use the equation estimated in part (c) to predict the landscaping expenditures for a home valued at $\$575,000.$ $$

Production Line Speed and Quality Control. Brawdy Plastics, Inc., produces plastic seat belt retainers for General Motors at their plant in Buffalo, New York. After final assembly and painting, the parts are placed on a conveyor belt that moves the parts past a final inspection station. How fast the parts move past the final inspection station depends upon the line speed of the conveyor belt (feet per minute). Although faster line speeds are desirable, management is concerned that increasing the line speed too much may not provide enough time for inspectors to identify which parts are actually defective. To test this theory, Brawdy Plastics conducted an experiment in which the same batch of parts, with a known number of defective parts, was inspected using a variety of line speeds. The following data were collected.

Number of

$$\begin{array}{cc}\text { Line } & \text { Defective } \\ \text { Speed } & \begin{array}{c}\text { Dumber of } \\ \text { Parts Found }\end{array} \\ 20 & 23 \\ 20 & 21 \\ 30 & 19 \\ 30 & 16 \\ 40 & 15 \\ 40 & 17 \\ 50 & 14 \\ 50 & 11\end{array}$$

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

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.