EXAMPLE 3. Sam is interested in predicting the amount of time it takes him to write a report (minutes) based on its word count. He randomly selects 7 reports and records the amount of time it took him to write each report and the corresponding word count. Given the following table of additional information: 1,606 909 |1,222,691 130,988 E (; – 2)(y; – ) 298,909 Identify, in words, the dependent variable. a. X = a report's word count O b. Y = a report's word count c. Y = amount of time it takes Sam to write a report (minutes) d. X = amount of time it takes Sam to write a report (minutes) Calculate the standard deviation of X. a. 494.5080 b. 417.9356 c. 390.9429 d. None of the other choices

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Hi, I would appreciate if you could help me with the following questions please.

### Correlation and Determination Quiz

#### Question 1: Find the correlation coefficient between X and Y.
Choose one of the following options:
- a. None of the other choices
- b. 0.8410
- c. 0.6402
- d. 0.7469

#### Question 2: What is the direction of the linear association?
Choose one of the following options:
- a. None of the other choices
- b. Weak
- c. Strong
- d. Moderate

#### Question 3: Calculate the coefficient of determination.
Choose one of the following options:
- a. 0.5579
- b. None of the other choices
- c. 0.4099
- d. 0.7073

#### Question 4: Determine the least squares regression equation.
Choose one of the following options:
- a. \(\hat{y} = 516.3330 + 0.2445x\)
- b. \(\hat{y} = -2755.8231 + 2.282x\)
- c. \(\hat{y} = 1383.7785 + 0.2445x\)
- d. \(\hat{y} = -468.299 + 2.282x\)
Transcribed Image Text:### Correlation and Determination Quiz #### Question 1: Find the correlation coefficient between X and Y. Choose one of the following options: - a. None of the other choices - b. 0.8410 - c. 0.6402 - d. 0.7469 #### Question 2: What is the direction of the linear association? Choose one of the following options: - a. None of the other choices - b. Weak - c. Strong - d. Moderate #### Question 3: Calculate the coefficient of determination. Choose one of the following options: - a. 0.5579 - b. None of the other choices - c. 0.4099 - d. 0.7073 #### Question 4: Determine the least squares regression equation. Choose one of the following options: - a. \(\hat{y} = 516.3330 + 0.2445x\) - b. \(\hat{y} = -2755.8231 + 2.282x\) - c. \(\hat{y} = 1383.7785 + 0.2445x\) - d. \(\hat{y} = -468.299 + 2.282x\)
**EXAMPLE 3**

Sam is interested in predicting the amount of time it takes him to write a report (minutes) based on its word count. He randomly selects 7 reports and records the amount of time it took him to write each report and the corresponding word count. Given the following table of additional information:

| Statistic                                                   | Value   |
|-------------------------------------------------------------|---------|
| \(\bar{x}\) (Mean of X)                                      | 1,606   |
| \(\bar{y}\) (Mean of Y)                                      | 909     |
| \(\sum_{i=1}^{n} (x_i - \bar{x})^2\) (Sum of squared deviations of X) | 1,222,691 |
| \(\sum_{i=1}^{n} (y_i - \bar{y})^2\) (Sum of squared deviations of Y) | 130,988   |
| \(\sum_{i=1}^{n} (x_i - \bar{x})(y_i - \bar{y})\) (Sum of products of deviations) | 298,909   |

**Identify, in words, the dependent variable.**

- ○ a. X = a report's word count
- ○ b. Y = a report's word count
- ○ c. Y = amount of time it takes Sam to write a report (minutes)
- ○ d. X = amount of time it takes Sam to write a report (minutes)

**Calculate the standard deviation of X.**

- ○ a. 494.5080
- ○ b. 417.9356
- ○ c. 390.9429
- ○ d. None of the other choices
Transcribed Image Text:**EXAMPLE 3** Sam is interested in predicting the amount of time it takes him to write a report (minutes) based on its word count. He randomly selects 7 reports and records the amount of time it took him to write each report and the corresponding word count. Given the following table of additional information: | Statistic | Value | |-------------------------------------------------------------|---------| | \(\bar{x}\) (Mean of X) | 1,606 | | \(\bar{y}\) (Mean of Y) | 909 | | \(\sum_{i=1}^{n} (x_i - \bar{x})^2\) (Sum of squared deviations of X) | 1,222,691 | | \(\sum_{i=1}^{n} (y_i - \bar{y})^2\) (Sum of squared deviations of Y) | 130,988 | | \(\sum_{i=1}^{n} (x_i - \bar{x})(y_i - \bar{y})\) (Sum of products of deviations) | 298,909 | **Identify, in words, the dependent variable.** - ○ a. X = a report's word count - ○ b. Y = a report's word count - ○ c. Y = amount of time it takes Sam to write a report (minutes) - ○ d. X = amount of time it takes Sam to write a report (minutes) **Calculate the standard deviation of X.** - ○ a. 494.5080 - ○ b. 417.9356 - ○ c. 390.9429 - ○ d. None of the other choices
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