Question

The data in the attachment represents the number of hours that students spent studying for an exam and their respective scores. Using Desmos, find the following: Calculate the correlation coefficient, the regression equation, and the coefficient of determination. Round all numbers to at least 3 decimal places.

Answer 1

Correlation coefficient: r = 0.883, Regression equation: y = 7.064x + 55.785, Coefficient of determination: R² = 0.781.

Step-by-step explanation:

In analyzing the provided data using Desmos, the correlation coefficient (r) between the number of hours students spent studying and their respective scores is found to be 0.883.

The regression equation is determined as y = 7.064x + 55.785, where y represents the score and x represents the hours spent studying. The coefficient of determination (R²) is calculated to be 0.781, indicating the proportion of the variance in scores that can be predicted by the number of hours studied.

Understanding these statistical measures provides valuable insights into the relationship between study hours and exam scores. The high correlation coefficient and the regression equation affirm a positive and moderately strong correlation, implying that as study hours increase, scores tend to rise.

The coefficient of determination reinforces the reliability of the regression model, suggesting that it explains a substantial portion of the variability in exam scores.