Q: A regional sales manager uses the regression line $$y = 284x - 16,101 to $$predict sales. If a salesperson contacts 6 clients, what is the predicted sales amount?

$$y = 284 \times 6 - 16,101 = -14,425$$

Question 1

Which of the following statements best describes the meaning of the correlation coefficient $$r in a $$dataset?

Accepted Answer

It measures the strength and direction of the linear relationship between two variables.

Question 2

A scatterplot of test scores versus time spent studying shows points closely clustered around a straight line with a positive slope. What type of correlation is present?

Accepted Answer

Positive linear correlation

Question 3

Which equation represents the least squares regression line for a dataset?

Accepted Answer

$$y = b_1$ x + b_0$

Question 4

A marketing researcher finds $$r = 0.59$$ for the relationship between advertising budget and sales revenue. What does this value indicate?

Accepted Answer

There is a moderate positive linear correlation.

Question 5

Which of the following is the correct formula for the coefficient of determination $$R^2$$?

Accepted Answer

$$R^2$$ = $$r^2$$

Question 6

If $$r = -0.957$$ for a dataset, what percentage of the variation in the dependent variable is explained by the independent variable?

Accepted Answer

About 91.6%

Question 7

Which of the following statements is true regarding residuals in regression analysis?

Accepted Answer

Residuals are the vertical distance from a point to the regression line.

Question 8

A residual plot shows random scatter around zero. What does this indicate about the regression model?

Accepted Answer

The model is a good fit for the data.

Question 9

Which hypothesis test is used to determine if the slope of a regression line is significantly different from zero?

Accepted Answer

F:LinRegTTest

Question 10

A prediction interval for weekly revenue from $$200 in ad spending is (520$$, $610). What does this interval mean?

Accepted Answer

We are 95% confident that a single weekly revenue value with $$200 in ad spending will fall between 520 $$and $610.

Question 11

Which of the following best describes the phrase 'correlation does NOT imply causation'?

Accepted Answer

Two variables can be correlated without one causing the other.

Question 12

A quadratic regression equation has the form:

Accepted Answer

$$y = a x^2$ + b x + c$$

Question 13

In a hypothesis test for the population correlation coefficient $$\rho$$, which null hypothesis is used to test for no correlation?

Accepted Answer

$$H_0$$: \rho = 0$$

Question 14

A regional sales manager uses the regression line $$y = 284x - 16,101 to $$predict sales. If a salesperson contacts 6 clients, what is the predicted sales amount?

Accepted Answer

$$y = 284 	imes 6 - 16,101 = -14,425$$

Question 15

Which of the following is NOT a plausible reason for a weak correlation between advertising budget and sales revenue?

Accepted Answer

Perfect linear relationship

Question 16

If the coefficient of determination $$R^2 is $$close to 1, what does this indicate?

Accepted Answer

Almost all of the variation is explained by the linear relationship.

Question 17

Which calculator function is used to perform quadratic regression?

Accepted Answer

5:QuadReg

Question 18

A residual plot shows a clear pattern (e.g., oscillating or diverging). What does this suggest about the regression model?

Accepted Answer

The model is not a good fit for the data.

Question 19

Which of the following best describes the use of a regression line for prediction?

Accepted Answer

Use the regression line only if the correlation is strong and the $$x-$$value is within the range of the data.

Question 20

A quadratic regression model is preferred over a linear model when:

Accepted Answer

The data points form a curve rather than a straight line.

Chapter 10: Correlation and Regression – Study Notes

Guida di studio - Domande di pratica

Study guide - Flashcard