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A researcher is examining the relationship between stress levels and performance on a test of cognitive performance. She hypothesizes that stress levels lead to an increase in performance to a point, and then increased stress decreases performance. She tests 10 participants who have the following levels of stress: 10.94 12.76 7.62 8.17 7.83 12.22 9.23 11.17 11.88 8.18 When she tests their levels of mental performance, she finds the following cognitive performance scores (listed in the same participant order as above):  5.24  4.64  4.68 5.04 4.17 6.20  4.54  6.55 5.79  3.17 Perform a linear regression to examine the relationship between these variables. What do the results mean?

A researcher is examining the relationship between stress levels and performance on a test of cognitive performance. She hypothesizes that stress levels lead to an increase in performance to a point, and then increased stress decreases performance. She tests 10 participants who have the following levels of stress: 10.94 12.76 7.62 8.17 7.83 12.22 9.23 11.17 11.88 8.18 When she tests their levels of mental performance, she finds the following cognitive performance scores (listed in the same participant order as above):  5.24  4.64  4.68 5.04 4.17 6.20  4.54  6.55 5.79  3.17 Perform a linear regression to examine the relationship between these variables. What do the results mean?

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
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 A researcher is examining the relationship between stress levels and performance on a test of cognitive performance. She hypothesizes that stress levels lead to an increase in performance to a point, and then increased stress decreases performance. She tests 10 participants who have the following levels of stress:

10.94

12.76

7.62

8.17

7.83

12.22

9.23

11.17

11.88

8.18

When she tests their levels of mental performance, she finds the following cognitive performance scores (listed in the same participant order as above):

 5.24

 4.64

 4.68

5.04

4.17

6.20

 4.54

 6.55

5.79

 3.17

Perform a linear regression to examine the relationship between these variables. What do the results mean?

**Linear Regression** **Model Summary - V10.94** | Model | R | R² | Adjusted R² | RMSE | |-------|-------|-------|-------------|------| | H₀ | 0.000 | 0.000 | 0.000 | 2.091| | H₁ | 0.555 | 0.308 | 0.210 | 1.859| --- **ANOVA** | Model | Sum of Squares | df | Mean Square | F | p | |-------|----------------|----|-------------|-------|-------| | H₁ | 10.789 | 1 | 10.789 | 3.122 | 0.121 | | Residual | 24.189 | 7 | 3.456 | | | | Total | 34.979 | 8 | | | | *Note: The intercept model is omitted, as no meaningful information can be shown.* --- **Coefficients** | Model | Unstandardized | Standard Error | Standardized | t | p | |-------|----------------|----------------|--------------|-------|-------| | H₀ | (Intercept) 9.896 | 0.697 | | 14.197| < .001| | H₁ | (Intercept) 4.590 | 3.066 | | 1.497 | 0.178 | | | V5.24 1.076 | 0.609 | 0.555 | 1.767 | 0.121 | This summary provides information about two models: a null hypothesis model (H₀) and an alternative hypothesis model (H₁). The R, R², adjusted R², and RMSE values indicate the fit of each model. The ANOVA table displays the sum of squares for regression and residuals, with corresponding degrees of freedom (df) and p-values. The coefficients table provides details about the unstandardized and standardized coefficients, standard errors, t-values, and significance levels for each variable in the models.
Transcribed Image Text:**Linear Regression** **Model Summary - V10.94** | Model | R | R² | Adjusted R² | RMSE | |-------|-------|-------|-------------|------| | H₀ | 0.000 | 0.000 | 0.000 | 2.091| | H₁ | 0.555 | 0.308 | 0.210 | 1.859| --- **ANOVA** | Model | Sum of Squares | df | Mean Square | F | p | |-------|----------------|----|-------------|-------|-------| | H₁ | 10.789 | 1 | 10.789 | 3.122 | 0.121 | | Residual | 24.189 | 7 | 3.456 | | | | Total | 34.979 | 8 | | | | *Note: The intercept model is omitted, as no meaningful information can be shown.* --- **Coefficients** | Model | Unstandardized | Standard Error | Standardized | t | p | |-------|----------------|----------------|--------------|-------|-------| | H₀ | (Intercept) 9.896 | 0.697 | | 14.197| < .001| | H₁ | (Intercept) 4.590 | 3.066 | | 1.497 | 0.178 | | | V5.24 1.076 | 0.609 | 0.555 | 1.767 | 0.121 | This summary provides information about two models: a null hypothesis model (H₀) and an alternative hypothesis model (H₁). The R, R², adjusted R², and RMSE values indicate the fit of each model. The ANOVA table displays the sum of squares for regression and residuals, with corresponding degrees of freedom (df) and p-values. The coefficients table provides details about the unstandardized and standardized coefficients, standard errors, t-values, and significance levels for each variable in the models.
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