Final answer:
Confidence intervals for the marginal and partial slopes refer to simple and multiple linear regression respectively. The 95% confidence interval for the partial slope is given but the interval for the marginal slope is absent, preventing direct comparison. Confidence intervals' width reflects certainty, with a 90% interval being narrower and a 99% interval wider than a 95% interval.
Step-by-step explanation:
When comparing the confidence intervals for the marginal slope and the partial slope for file size, first consider that these two types of slopes arise from different types of analyses in regression modeling. The marginal slope is taken from a simple linear regression where only one predictor (file size) is considered in relation to the outcome (response variable), without controlling for the effects of other variables. On the other hand, the partial slope represents the relationship between the predictor (file size) and the response variable in the context of a multiple linear regression, where the effects of other predictors are controlled for.
Based on the student's data, the marginal slope's 95% confidence interval is not provided, so it can't be directly compared here. However, the student indicated that the 95% confidence interval for the partial slope is from -0.03 to 0.68. The concept of confidence intervals implies that a wider interval suggests more uncertainty about the estimate, whereas a narrower interval suggests a more precise estimate. The exact comparison between these two confidence intervals requires the missing information for the marginal slope.
Understanding confidence intervals is critical: the larger the confidence level, the wider the interval needs to be to ensure that it captures the true parameter value. For example, a 99% confidence interval would be wider than a 95% confidence interval because it is designed to contain the true parameter value with a higher degree of certainty. Consequently, a 90% confidence interval would be narrower as it contains less area under the normal distribution curve and reflects less certainty. Both intervals have two possibilities: either they contain the true parameter or they do not, with the likelihood mirroring the confidence level (95% for a 95% interval, 99% for a 99% interval, etc.).