A, T= , P-value ### Exploring the Relationship Between Beauty and Teaching EvaluationsIn the following exercise, visually check the conditions for fitting a least squares regression line. However, you do not need to report these conditions in your solutions.Many college courses conclude by giving students the opportunity to evaluate the course and the instructor anonymously. The use of these student evaluations as an indicator of course quality and teaching effectiveness is often criticized because these measures may reflect the influence of non-teaching related characteristics, such as the physical appearance of the instructor.Researchers at the University of Texas, Austin collected data on teaching evaluation scores (higher scores mean better) and standardized beauty scores (a score of 0 means average, negative scores mean below average, and a positive score means above average) for a sample of 463 professors. The scatterplot below shows the relationship between these variables, and also provides a regression output for predicting teaching evaluation scores from beauty scores.#### ScatterplotThe scatterplot displays teaching evaluation scores against beauty scores, revealing a slight positive trend. #### Regression ResultsBelow the scatterplot, a table provides the summary of the regression model used to predict teaching evaluation scores based on beauty scores.| | Estimate | Std. Error | t value | Pr(>|t|) ||--------------|----------|------------|----------|---------|| (Intercept) | 4.010 | 0.0255 | 157.21 | 0.0000 || beauty | 0.0322 | 0.0078 | 4.13 | 0.0000 |#### Questions and Instructions for Analysis##### (a) Calculation of the Slope**Prompt:** Given that the average standardized beauty score is -0.0883 and the average teaching evaluation score is 3.9983, calculate the slope. Alternatively, the slope may be computed using just the information provided in the model summary table. (Round your answer to four decimal places.)#### Answer:The slope from the model summary table is already calculated as 0.0322.##### (b) Evaluating the Evidence**Prompt:** Do these data provide convincing evidence that the slope of the relationship between teaching evaluation and beauty is positive? Explain your reasoning.- **State the appropriate null and alternative hypotheses.** Let's state our hypotheses: - $ H_0: \beta_{\text{beauty}} = 0 $

Many college courses conclude by giving students the opportunity to evaluate the course and the instructor anonymously. However, the use of these student evaluations as an indicator of course quality and teaching effectiveness is often criticized because these measures may reflect the influence of non-teaching related characteristics, such as the physical appearance of the instructor. Researchers at University of Texas, Austin collected data on teaching evaluation score (higher score means better) and standardized beauty score (a score of 0 means average, negative score means below average, and a positive score means above average) for a sample of 463 professors. The scatterplot below shows the relationship between these variables, and also provided is a regression output for predicting teaching evaluation score from beauty score. Beauty Estimate Std. Error t value Pr(>It|) (Intercept) 4.010 0.0255 157.21 0.0000 beauty 0.0322 4.13 0.0000 (a) Given that the average standardized beauty score is -0.0883 and average teaching evaluation score is 3.9983, calculate the slope. Alternatively, the slope may be computed using just the information provided in the model summary table. (Round your answer to four decimal places.)

Many college courses conclude by giving students the opportunity to evaluate the course and the instructor anonymously. However, the use of these student evaluations as an indicator of course quality and teaching effectiveness is often criticized because these measures may reflect the influence of non-teaching related characteristics, such as the physical appearance of the instructor. Researchers at University of Texas, Austin collected data on teaching evaluation score (higher score means better) and standardized beauty score (a score of 0 means average, negative score means below average, and a positive score means above average) for a sample of 463 professors. The scatterplot below shows the relationship between these variables, and also provided is a regression output for predicting teaching evaluation score from beauty score. Beauty Estimate Std. Error t value Pr(>It|) (Intercept) 4.010 0.0255 157.21 0.0000 beauty 0.0322 4.13 0.0000 (a) Given that the average standardized beauty score is -0.0883 and average teaching evaluation score is 3.9983, calculate the slope. Alternatively, the slope may be computed using just the information provided in the model summary table. (Round your answer to four decimal places.)

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Question

A, T= , P-value

### Exploring the Relationship Between Beauty and Teaching Evaluations

In the following exercise, visually check the conditions for fitting a least squares regression line. However, you do not need to report these conditions in your solutions.

Many college courses conclude by giving students the opportunity to evaluate the course and the instructor anonymously. The use of these student evaluations as an indicator of course quality and teaching effectiveness is often criticized because these measures may reflect the influence of non-teaching related characteristics, such as the physical appearance of the instructor.

Researchers at the University of Texas, Austin collected data on teaching evaluation scores (higher scores mean better) and standardized beauty scores (a score of 0 means average, negative scores mean below average, and a positive score means above average) for a sample of 463 professors. The scatterplot below shows the relationship between these variables, and also provides a regression output for predicting teaching evaluation scores from beauty scores.

#### Scatterplot
The scatterplot displays teaching evaluation scores against beauty scores, revealing a slight positive trend.

#### Regression Results
Below the scatterplot, a table provides the summary of the regression model used to predict teaching evaluation scores based on beauty scores.

| | Estimate | Std. Error | t value | Pr(>|t|) |
|--------------|----------|------------|----------|---------|
| (Intercept) | 4.010 | 0.0255 | 157.21 | 0.0000 |
| beauty | 0.0322 | 0.0078 | 4.13 | 0.0000 |

#### Questions and Instructions for Analysis

##### (a) Calculation of the Slope
**Prompt:**
Given that the average standardized beauty score is -0.0883 and the average teaching evaluation score is 3.9983, calculate the slope. Alternatively, the slope may be computed using just the information provided in the model summary table. (Round your answer to four decimal places.)

#### Answer:
The slope from the model summary table is already calculated as 0.0322.

##### (b) Evaluating the Evidence
**Prompt:**
Do these data provide convincing evidence that the slope of the relationship between teaching evaluation and beauty is positive? Explain your reasoning.

- **State the appropriate null and alternative hypotheses.**

Let's state our hypotheses:
- $ H_0: \beta_{\text{beauty}} = 0 $

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