**Investigating the Relationship Between Temperature and Ice Cream Sales**We are interested in determining if the temperature affects ice cream sales. The following data from 10 days is provided:| Temperature | Sales ||-------------|-------|| 58 | 215 || 53 | 185 || 59 | 332 || 65 | 406 || 72 | 522 || 67 | 412 || 77 | 614 || 74 | 544 || 65 | 421 || 73 | 445 |**Analysis Questions:**a. **Identify Variables:** - Which one is the independent variable and which one is the dependent variable?b. **Calculate the Slope (b₁):** - Find $ b_1 $.c. **Calculate the Intercept (b₀):** - Find $ b_0 $.d. **Total Sum of Squares (SST):** - Find SST.e. **Regression Sum of Squares (SSR):** - Find SSR.f. **Error Sum of Squares (SSE):** - Find SSE.g. **Coefficient of Determination:** - Find the coefficient of determination.h. **Correlation Coefficient:** - Find the correlation coefficient.i. **Variance of Residuals (s²):** - Find $ s^2 $.j. **Test Statistic for Slope (b₁):** - Find the test statistic for testing if $ b_1 $ is significant or not.k. **Conclusion Based on Test Statistic:** - What conclusion would you make based on the test statistic found above (use a 0.05 confidence level)?l. **95% Confidence Interval for Slope (b₁):** - Find the 95% confidence interval for $ b_1 $.m. **Expected Sales at 80 Degrees:** - Assuming the temperature is 80, how much would you expect ice cream sales to be?n. **90% Confidence Interval for Expected Sales at 80 Degrees:** - Assuming the temperature is 80, what is the 90% confidence interval for the expected ice cream sales?o. **90% Prediction Interval for Expected Sales at 80 Degrees:** -

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Description: **Investigating the Relationship Between Temperature and Ice Cream Sales**We are interested in determining if the temperature affects ice cream sales. The following data from 10 days is provided:| Temperature | Sales ||-------------|-------|| 58

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We are interested in determining if the temperature affects ice cream sales. The following data from 10 days is provided Sales Temperature 58 53 59 65 215 185 332 406 72 522 67 77 412 614 74 544 65 421 445 73 a. Which one is the independent variable and which one is the dependent variable? b. Find b,. c. Find bo-

We are interested in determining if the temperature affects ice cream sales. The following data from 10 days is provided Sales Temperature 58 53 59 65 215 185 332 406 72 522 67 77 412 614 74 544 65 421 445 73 a. Which one is the independent variable and which one is the dependent variable? b. Find b,. c. Find bo-

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Mean, Median, Mode

It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.

Z-Scores

A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.

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Question

**Investigating the Relationship Between Temperature and Ice Cream Sales**

We are interested in determining if the temperature affects ice cream sales. The following data from 10 days is provided:

| Temperature | Sales |
|-------------|-------|
| 58 | 215 |
| 53 | 185 |
| 59 | 332 |
| 65 | 406 |
| 72 | 522 |
| 67 | 412 |
| 77 | 614 |
| 74 | 544 |
| 65 | 421 |
| 73 | 445 |

**Analysis Questions:**

a. **Identify Variables:**
- Which one is the independent variable and which one is the dependent variable?

b. **Calculate the Slope (b₁):**
- Find $ b_1 $.

c. **Calculate the Intercept (b₀):**
- Find $ b_0 $.

d. **Total Sum of Squares (SST):**
- Find SST.

e. **Regression Sum of Squares (SSR):**
- Find SSR.

f. **Error Sum of Squares (SSE):**
- Find SSE.

g. **Coefficient of Determination:**
- Find the coefficient of determination.

h. **Correlation Coefficient:**
- Find the correlation coefficient.

i. **Variance of Residuals (s²):**
- Find $ s^2 $.

j. **Test Statistic for Slope (b₁):**
- Find the test statistic for testing if $ b_1 $ is significant or not.

k. **Conclusion Based on Test Statistic:**
- What conclusion would you make based on the test statistic found above (use a 0.05 confidence level)?

l. **95% Confidence Interval for Slope (b₁):**
- Find the 95% confidence interval for $ b_1 $.

m. **Expected Sales at 80 Degrees:**
- Assuming the temperature is 80, how much would you expect ice cream sales to be?

n. **90% Confidence Interval for Expected Sales at 80 Degrees:**
- Assuming the temperature is 80, what is the 90% confidence interval for the expected ice cream sales?

o. **90% Prediction Interval for Expected Sales at 80 Degrees:**
-

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