The value y (in 1982–1984 dollars) of each dollar paid by consumers in each of the years from 1994 through 2008 in a country is represented by the ordered pairs.
(1994, 0.678)    	    (1995, 0.656)
(1996, 0.637)    	    (1997, 0.628)
(1998, 0.610)    	    (1999, 0.599)
(2000, 0.580)    	    (2001, 0.567)
(2002, 0.557)    	    (2003, 0.541)
(2004, 0.524)    	    (2005, 0.508)
(2006, 0.495)    	    (2007, 0.486)
(2008, 0.460)    	    
(a) Use a spreadsheet software program to generate a scatter plot of the data. Let 
t = 4
 represent 1994. Do the data appear linear?
Yes
No    
Incorrect: Your answer is incorrect.

(b) Use the regression feature of the spreadsheet software program to find a linear model for the data. (Let t represent time. Round your numerical values to four decimal places.)
y = 
  
Incorrect: Your answer is incorrect.


(c) Use the model to predict the value (in 1982–1984 dollars) of 1 dollar paid by consumers in 2010 and in 2011. (Round your answers to two decimal places.)
2010    	$ 
2011	$ 


Discuss the reliability of your predictions based on your scatter plot and the graph of your linear model for the data.
Because the data does not follow a linear pattern, the predictions for 2010 and 2011 are reliable.
Because the data follow a linear pattern, the predictions for 2010 and 2011 are not reliable.    
Because the data follow a linear pattern, the predictions for 2010 and 2011 are reliable.
Because the data does not follow a linear pattern, the predictions for 2010 and 2011 are not reliable.
Correct: Your answer is correct.


Let's work through each part of the problem step-by-step.

### (a) Scatter Plot and Linear Appearance

1. **Scatter Plot**: To create the scatter plot, plot each year against the corresponding value of each dollar (in 1982–1984 dollars). Specifically, the x-axis should represent the year (starting at 1994 with $ t = 4 $) and the y-axis should represent the value of a dollar.

2. **Linear Appearance**: By observing the scatter plot, determine whether the points approximately form a straight line. If the points lie roughly along a straight line, the data is linear; otherwise, it is not.

### (b) Finding the Linear Model

To find the linear model, use the regression feature of a spreadsheet program. Here’s the general approach:

1. **Data Transformation**: Define $ t $ as the number of years since 1990, so for 1994, $ t = 4 $.
   
2. **Linear Regression**: Use the data points $(t, y)$ to find a linear regression line in the form:
   \[
   y = mt + b
   \]
   where:
   - $ m $ is the slope of the line.
   - $ b $ is the y-intercept.

3. **Finding the Coefficients**: Use the spreadsheet regression tool to find the values of $ m $ and $ b $. Make sure to round these values to four decimal places.

### (c) Predicting the Value for 2010 and 2011

1. **Years Transformation**:
   - For 2010, $ t = 20 $ (since $ 2010 - 1990 = 20 $).
   - For 2011, $ t = 21 $ (since $ 2011 - 1990 = 21 $).

2. **Use the Model**:
   Substitute $ t = 20 $ and $ t = 21 $ into the linear model $ y = mt + b $ to find the predicted values for 2010 and 2011.

3. **Rounding**: Round the results to two decimal places.

### Discussion on Reliability

- **Reliability of the Model**: Assess whether the predictions are reliable by comparing the linear model's line with the scatter plot data points.
- If the data points closely follow a straight line, then predictions from the linear model are reliable.
- If the data points do not follow a straight line, then the predictions are not reliable.

### Example Calculation:

To illustrate the process, let's calculate step-by-step using regression calculations manually or by using appropriate software. For the spreadsheet, you would typically use functions like LINEST in Excel or similar features in Google Sheets.

1. Input the given years and values.
2. Define $ t $ values based on the given years.
3. Use the regression feature to find the coefficients.
4. Substitute these coefficients into the linear equation.
5. Calculate the predicted values for $ t = 20 $ (2010) and $ t = 21 $ (2011).

Would you like me to simulate the regression calculation and find the exact values for $ m $ and $ b $ using your data?

The value y (in 1982–1984 dollars) of each dollar paid by consumers in each of the years from 1994 through 2008 in a country is represented by the ordered pairs. (1994, 0.678) (1995, 0.656) (1996, 0.637) (1997, 0.628) (1998, 0.610) (1999, 0.599) (2000, 0.580) (2001, 0.567) (2002, 0.557) (2003, 0.541) (2004, 0.524) (2005, 0.508) (2006, 0.495) (2007, 0.486) (2008, 0.460) (a) Use a spreadsheet software program to generate a scatter plot of the data. Let t = 4 represent 1994. Do the data appear linear? (b) Use the regression feature of the spreadsheet software program to find a linear model for the data. (c) Use the model to predict the value of 1 dollar paid by consumers in 2010 and 2011.

Analyze the decline in dollar value from 1994 to 2008 using linear regression. Learn how to create a scatter plot and find a linear model to predict future values. Includes a step-by-step guide on using regression to forecast dollar value for 2010 and 2011.

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