Question 1

Which of the following best describes the term 'linear regression' in statistics?

Accepted Answer

A method for finding the straight line that best fits the pattern of the data by minimizing the sum of squared residuals.

Question 2

Suppose you are given the regression equation $$y = 85 + 188x. $$What does the number 85 represent in this context?

Accepted Answer

The predicted value of $$y$$ when $$x = 0.$$

Question 3

A scatterplot is a graph of paired $$(x, y)$$ data. What type of data does a scatterplot best represent?

Accepted Answer

Quantitative data

Question 4

Given the following paired data for serving size (oz) and saturated fat (grams): $$\begin{array}{cc} 9 & 8 \ 12 & 10 \ 14 & 11 \ 13 & 13 \ 15 & 15 \end{array}$$, which scatterplot best represents the relationship?

Accepted Answer

A scatterplot with points trending upward from left to right.

Question 5

If the correlation coefficient $$r$$ for a data set is $$0.92$$ and the critical value for $$n = 5 is$$ $$0.878$$, what can you conclude about the linear relationship?

Accepted Answer

There is sufficient evidence to support the claim of a linear relationship.

Question 6

Given the ID numbers: $$36, 42, 16, 50, 6, 24, 61, 35, 8, 44, 19, 23, 67, 20$$, what is the median?

Accepted Answer

$$30$$

Question 7

What does the mode represent in a data set?

Accepted Answer

The value that appears most frequently in the data set.

Question 8

If the mean of a data set is $$30$$ and the standard deviation is $$5$$, what is the boundary for significantly low values (using $$\mu - 2\sigma$$)?

Accepted Answer

$$20$$

Question 9

A body mass index (BMI) of $$23.2 is $$being evaluated for significance. If the mean BMI is $$22$$ and the standard deviation is $$1$$, is $$23.2$$ significantly high, not significant, or significantly low?

Accepted Answer

Not significant

Question 10

Given a mean body length of $$46$$ inches and a standard deviation of $$2$$ inches, what is the $$z-$$score for a body length of $$48.6$$ inches?

Accepted Answer

$$1.3$$

Question 11

If a $$z-$$score is between $$-2$$ and $$2$$, what does this indicate about the data value?

Accepted Answer

It is not significant.

Question 12

What is the difference between the mean and the median in a data set?

Accepted Answer

The mean is the average of all values, while the median is the middle value when the data is ordered.

Question 13

If the correlation coefficient $$r is$$ $$0.5$$ and the critical value is $$0.811$$, what is the conclusion?

Accepted Answer

There is not sufficient evidence to support the claim of a linear coefficient.

Question 14

A student divides $$4.27 by$$ $$0.83. $$What is the result rounded to the nearest hundredth?

Accepted Answer

$$5.15$$

Question 15

Which of the following best describes a positive linear relationship in a scatterplot?

Accepted Answer

As $$x$$ increases, $$y$$ also increases.

Question 16

If a data set has no mode, what does this mean?

Accepted Answer

No value appears more than once in the data set.

Question 17

Which of the following is NOT a correct interpretation of the spread of student ID numbers in a sample?

Accepted Answer

The mean and mode always give the same value for the spread.

Question 18

If the mean is $$50$$ and the standard deviation is $$8$$, what is the boundary for significantly high values (using $$\mu + 2\sigma$$)?

Accepted Answer

$$66$$

Question 19

Which of the following statements about the correlation coefficient $$r is $$correct?

Accepted Answer

$$r$$ measures the strength and direction of a linear relationship between two quantitative variables.

Question 20

A data set has a mean of $$100$$ and a standard deviation of $$15. $$What is the $$z-$$score for a value of $$130$$?

Accepted Answer

$$2$$

Question 21

If a scatterplot shows no apparent pattern, what can you conclude about the relationship between the variables?

Accepted Answer

There is no linear relationship between the variables.

Statistics Study Guide: Correlation, Regression, Measures of Central Tendency, and Z-Scores

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