Question: What percentage of the variation in grades is explained by studytime andmethod?a. 8.79 %b. 35.52 %c. 59.6 %d. 77.2 %

To determine the percentage of variation in grades explained by study time and method, we generally need access to data from a statistical analysis, such as the coefficients of determination (R²) from a regression analysis. However, since these options are given, I will guide you through the process to identify the correct answer based on typical values.

1. Break Down the Problem

1. Understand that the options represent the R² value, which indicates how well the independent variables (study time and method) explain the variation in the dependent variable (grades).
2. Identify which of the provided percentages is likely to be the R² value from a similar context.

2. Relevant Concepts

• The R² value ranges from 0 to 1 (or 0% to 100%).
• A higher value of R² indicates a better fit of the model to the data and thus a greater proportion of variation explained.

3. Analysis and Detail

• The options provided suggest different scenarios of how studytime and method might impact grades:
  • a. 8.79 % – indicates a very weak relationship.
  • b. 35.52 % – suggests a moderate relationship.
  • c. 59.6 % – indicates a reasonably strong relationship.
  • d. 77.2 % – suggests a strong relationship.

Given educational contexts, it's common to observe that study time and methods can explain a significant portion of grade variation.

4. Verify and Summarize

If we assume typical scenarios from educational data:

• While 8.79% and 35.52% may be plausible, they indicate weaker relationships.
• Both 59.6% and 77.2% suggest strong relationships.
• However, 77.2% is quite high and would be exceptional in most analyses unless the data is highly structured.

Final Answer

Based on common expectations in educational research, the most likely answer is d. 77.2 % as it represents a strong explanatory power of study time and method on student grades.