Q: Given the regression equation $$y = 284x - 16,101$$, what is the predicted value of $$y$$ when $$x = 83$$?

$$y = 284 \times 83 - 16,101 = 7,471$$

Question 1

Which of the following best describes the meaning of the correlation coefficient $$r in $$the context of business statistics?

Accepted Answer

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

Question 2

A scatterplot of advertising spending and product sales shows points tightly clustered around an upward-sloping line. What can you conclude about the correlation coefficient $$r$$?

Accepted Answer

$$r is $$close to 1, indicating a strong positive linear correlation.

Question 3

Which statement is TRUE regarding the relationship between correlation and causation?

Accepted Answer

Correlation does not imply causation.

Question 4

Given the regression equation $$y = 284x - 16,101$$, what is the predicted value of $$y$$ when $$x = 83$$?

Accepted Answer

$$y = 284 	imes 83 - 16,101 = 7,471$$

Question 5

If the correlation coefficient $$r = -0.957$$, what is the coefficient of determination $$R^2$$?

Accepted Answer

$$R^2$$ = $$(-0.957)^2 = 0.916$

Question 6

A residual plot for a regression model shows a clear pattern. What does this indicate about the model?

Accepted Answer

The model is not a good fit for the data.

Question 7

Which of the following is minimized by the least squares regression method?

Accepted Answer

The sum of the squared residuals.

Question 8

If a regression line is used to predict $$y$$ for an $$x-$$value far outside the range of the data, what is the best practice?

Accepted Answer

Use the mean of $$y as $$the best estimate.

Question 9

Which function on a TI-84 calculator is used to perform a hypothesis test for the slope of a regression line?

Accepted Answer

LinRegTTest

Question 10

A business analyst finds $$r = 0.13$$ for the relationship between number of pins on a backpack and test scores. What does this indicate?

Accepted Answer

There is a very weak linear correlation between the variables.

Question 11

Which of the following best describes the coefficient of determination $$R^2$$?

Accepted Answer

$$R^2$$ measures the proportion of variation in $$y$$ explained by $$x in $$the regression model.

Question 12

A company wants to predict ice cream sales using the regression equation $$y = 222x - 11,111. If $$the high temperature is 80°F, what is the predicted sales value?

Accepted Answer

$$y = 222 	imes 80 - 11,111 = 6,649$$

Question 13

Which of the following is TRUE about the slope of the line of best fit and the correlation coefficient $$r$$?

Accepted Answer

The slope does not affect the value of $$r.$$

Question 14

A quadratic regression is more appropriate than a linear regression when:

Accepted Answer

The data shows a curved (nonlinear) pattern.

Question 15

If a 95% confidence interval for the slope of a regression line does NOT include 0, what does this suggest?

Accepted Answer

There is enough evidence to suggest a linear relationship between the variables.

Question 16

Which of the following is the correct formula for the margin of error $$E in a $$prediction interval for a regression line?

Accepted Answer

$$E = t_{\alpha/2} \cdot s_e \sqrt{1 + \frac{1}{n} + \frac{(x_0$ - \bar{x})^2$}{n \sum x^2$ - (\sum x)^2$}}$$

Question 17

A hypothesis test for the slope of a regression line is performed at $$\alpha = 0.05. $$The $$p-$$value is 0.03. What is the correct conclusion?

Accepted Answer

Reject $$H_0$$; there is enough evidence of a linear relationship.

Question 18

Which of the following is NOT a correct interpretation of $$R^2 = 0.80$ in a business context?

Accepted Answer

The correlation coefficient $$r$$ must be negative.

Question 19

Which calculator function should be used to perform a quadratic regression on a TI-84?

Accepted Answer

QuadReg

Correlation and Linear Regression: Study Notes for Business Statistics

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