Answer:
Q1: Interpretation of R2 value:
The R2 value, also known as the coefficient of determination, represents the proportion of the variance in the dependent variable (weight in grams) that can be explained by the independent variable (hours of sleep) in the linear regression model. In this case, an R2 value of 30.2% means that approximately 30.2% of the variability in weight can be explained by the hours of sleep.
Q2: Interpretation of the slope:
The slope in the equation represents the coefficient for the independent variable, which is the change in the weight (in grams) associated with a one-unit increase in the hours of sleep. In this case, the slope is 0.0606, indicating that for every additional hour of sleep, the weight is estimated to increase by 0.0606 grams.
Q3: Based on the this research, can she claim that hours of sleep causes weight gain? Briefly explain your answer.
Based on this research alone, it would be inappropriate to claim that hours of sleep causes weight gain. The regression analysis can only demonstrate an association between the two variables, not a causal relationship. While the study shows that there is a positive relationship between hours of sleep and weight (as indicated by the positive slope coefficient), there could be other confounding factors or variables that influence both sleep duration and weight gain. To establish causality, additional research with rigorous study designs and control of confounding variables is necessary.