2. The height of a bamboo shoot is measured at noon every day. The results for the first week are given in the table: x: day number y: height in inches 1 26.8 2 34.3 3 44.1 4 51.5 NOV 5 61.7 6 69.8 7 ert word 79.2 Note: you don't have to show your work in this problem; just indicate which software you have used to do the calculations. woled xod sill (a) find the coefficient of correlation between x and y; does the result indicate strong correlation?

MATLAB: An Introduction with Applications
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Need help on 2 a,b,c
**Educational Website Transcription:**

---

### Fall 2022 Mid-Term Exam

**2.**

**(b)** Find the regression equation giving the height \( y \) as a (linear) function of the day number \( x \).

- Write the regression equation in the box below:

  *[Box for answer]*

**(c)** Use the regression equation to predict the height of this bamboo shoot on day number 8.

- On day number 8, the height of the shoot is predicted to be **about** __________ inches.

**3.** Frank sews colorful pillows and sells them. His fixed cost is $40 per week, and the cost of the materials for one pillow is $5. Frank sells the pillows for $15 each. If \( x \) stands for the number of pillows made/sold in one week, then

**(a)** Write the weekly cost equation:

  *[Box for answer]*
  
**(b)** Write the weekly revenue equation:

  *[Box for answer]*

**(c)** Find the break-even point:

- Show the work above, and write your answer in the box below:

  *[Box for answer]*

**(d)** Find the profit that Frank would make if he sews and sells 15 pillows in one week:

- Show the work above, and write your answer in the box below:

  *[Box for answer]*

--- 

This document provides several algebraic exercises involving linear regression and cost-revenue-profit analysis, aimed at enhancing students' understanding of these concepts.
Transcribed Image Text:**Educational Website Transcription:** --- ### Fall 2022 Mid-Term Exam **2.** **(b)** Find the regression equation giving the height \( y \) as a (linear) function of the day number \( x \). - Write the regression equation in the box below: *[Box for answer]* **(c)** Use the regression equation to predict the height of this bamboo shoot on day number 8. - On day number 8, the height of the shoot is predicted to be **about** __________ inches. **3.** Frank sews colorful pillows and sells them. His fixed cost is $40 per week, and the cost of the materials for one pillow is $5. Frank sells the pillows for $15 each. If \( x \) stands for the number of pillows made/sold in one week, then **(a)** Write the weekly cost equation: *[Box for answer]* **(b)** Write the weekly revenue equation: *[Box for answer]* **(c)** Find the break-even point: - Show the work above, and write your answer in the box below: *[Box for answer]* **(d)** Find the profit that Frank would make if he sews and sells 15 pillows in one week: - Show the work above, and write your answer in the box below: *[Box for answer]* --- This document provides several algebraic exercises involving linear regression and cost-revenue-profit analysis, aimed at enhancing students' understanding of these concepts.
**Problem 2: Bamboo Shoot Growth Measurement**

The height of a bamboo shoot is measured at noon every day. The results for the first week are provided in the table below:

| x: Day Number | 1  | 2  | 3  | 4  | 5  | 6  | 7  |
|---------------|----|----|----|----|----|----|----|
| y: Height (in inches) | 26.8 | 34.3 | 44.1 | 51.5 | 61.7 | 69.8 | 79.2 |

**Instructions:**

Note: You do not need to show your work for this problem; just indicate which software you have used to do the calculations.

(a) Find the coefficient of correlation between x (day number) and y (height). Does the result indicate a strong correlation?

---

This problem is designed for students to apply knowledge of statistical correlation, particularly using software tools to compute and interpret the coefficient of correlation.
Transcribed Image Text:**Problem 2: Bamboo Shoot Growth Measurement** The height of a bamboo shoot is measured at noon every day. The results for the first week are provided in the table below: | x: Day Number | 1 | 2 | 3 | 4 | 5 | 6 | 7 | |---------------|----|----|----|----|----|----|----| | y: Height (in inches) | 26.8 | 34.3 | 44.1 | 51.5 | 61.7 | 69.8 | 79.2 | **Instructions:** Note: You do not need to show your work for this problem; just indicate which software you have used to do the calculations. (a) Find the coefficient of correlation between x (day number) and y (height). Does the result indicate a strong correlation? --- This problem is designed for students to apply knowledge of statistical correlation, particularly using software tools to compute and interpret the coefficient of correlation.
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