Q: Given the five-number summary: Minimum = 10, Q1 = 20, Median = 30, Q3 = 40, Maximum = 50, what is the interquartile range (IQR)?

$$\text{IQR} = Q_3$ - Q_1$ = 40 - 20 = 20$$

Q: Given the regression equation $$\hat{y} = 2 + 3x$$, what is the predicted value of $$y$$ when $$x = 4$$?

$$\hat{y} = 2 + 3 \times 4 = 14$$

Question 1

Which of the following best describes a 'case' in a statistical study?

Accepted Answer

A single observation or unit about which data are collected.

Question 2

A researcher collects data on students' test scores (numerical) and their favorite color (categorical). Which statement is correct regarding variable types?

Accepted Answer

Test scores are quantitative; favorite color is categorical.

Question 3

Given the five-number summary: Minimum = 10, Q1 = 20, Median = 30, Q3 = 40, Maximum = 50, what is the interquartile range (IQR)?

Accepted Answer

$$	ext{IQR} = Q_3$ - Q_1$ = 40 - 20 = 20$$

Question 4

Which statistic is considered 'resistant' to outliers?

Accepted Answer

Median

Question 5

A dataset is strongly skewed to the right. Which measure of center is most appropriate to report?

Accepted Answer

Median

Question 6

Which formula correctly calculates a z-score for a value $$x in a $$dataset with mean $$\mu$$ and standard deviation $$\sigma$$?

Accepted Answer

$$z = \frac{x - \mu}{\sigma}$$

Question 7

According to the Empirical Rule, what percentage of data falls within two standard deviations of the mean in a normal distribution?

Accepted Answer

Approximately 95%

Question 8

In a scatterplot showing the relationship between hours studied (x) and exam score (y), which variable is the explanatory variable?

Accepted Answer

Hours studied

Question 9

Which value of correlation coefficient $$r$$ indicates the strongest linear relationship?

Accepted Answer

$$r = -0.95$$

Question 10

Given the regression equation $$\hat{y} = 2 + 3x$$, what is the predicted value of $$y$$ when $$x = 4$$?

Accepted Answer

$$\hat{y} = 2 + 3 	imes 4 = 14$$

Question 11

What quantity is minimized in the method of least squares for linear regression?

Accepted Answer

$$\sum (y_i - \hat{y}_i)^2$

Question 12

If the standard error of the residuals ($$se) is $$much smaller than the standard deviation of $$y$$ ($$s_y$$), what does this indicate about the regression model?

Accepted Answer

The model is good for prediction.

Question 13

Which of the following best describes the interpretation of $$R^2 in $$regression analysis?

Accepted Answer

$$R^2 is $$the proportion of variation in the response variable explained by the explanatory variable.

Question 14

A boxplot shows a data set with a long whisker on the right side. What does this indicate about the shape of the data?

Accepted Answer

The data are skewed to the right.

Question 15

Which observation would be considered a moderate outlier according to the outlier boundaries?

Accepted Answer

A value beyond $$\pm 2$$ standard deviations from the mean.

Question 16

In regression diagnostics, what is a 'highly influential observation'?

Accepted Answer

An observation that greatly affects the slope and intercept of the regression line.

Question 17

A hospital wants to predict patient recovery time based on age. Which is the response variable?

Accepted Answer

Patient recovery time

Question 18

Which of the following is NOT a way to identify the shape of a data set?

Accepted Answer

Calculating the mean

Question 19

If a data set contains extreme values, which measure of spread is preferred?

Accepted Answer

Interquartile Range (IQR)

Question 20

A student scores 85 on a test where the mean is 80 and the standard deviation is 5. What is the student's z-score?

Accepted Answer

$$z = \frac{85 - 80}{5} = 1$$

Stat 240/250 Midterm Study Guide: Describing and Analyzing Quantitative Data & Regression

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