An electric device delivers a current of [tex]$15.0 A$[/tex] for 30 seconds. How many electrons flow through it?
Answer (1)
The problem provides linear regression results and asks for the line of best fit. The line of best fit is determined by substituting the given values of a and b into the equation y = a x + b . The correct equation should be y = − 3.1 x + 12.9 . However, none of the provided options match this equation, indicating a possible error in the options. Therefore, a definitive answer cannot be selected from the given choices.
Explanation
Understanding the Problem We are given the results of a linear regression performed on a set of data points. The linear regression output provides the equation of the line of best fit in the form y = a x + b , where a is the slope and b is the y-intercept. We are given the values a = − 3.1 and b = 12.9 . Our goal is to identify the correct equation of the line of best fit from the given options.
Substituting Values The general form of a linear equation is y = a x + b . In this case, the linear regression results tell us that a = − 3.1 and b = 12.9 . Substituting these values into the equation, we get y = − 3.1 x + 12.9 .
Comparing with Options Now, let's compare our equation with the given options: Option A: − 0.994 = − 3.1 x + 12.9 . This is incorrect because it sets the correlation coefficient r equal to the equation, which is not the line of best fit. Option B: y = − 0.994 x + 12.9 . This is incorrect because it uses the correlation coefficient r = − 0.994 as the slope instead of the value of a from the linear regression. Option C: y = 12.9 x − 3.1 . This is incorrect because it swaps the values of a and b , resulting in y = 12.9 x − 3.1 , which is not the line of best fit from the linear regression.
Finding the Best Match Based on the linear regression results, the line of best fit is y = − 3.1 x + 12.9 . However, none of the options exactly match this equation. It seems there might be a typo in the options or the provided values. However, based on the given information, the closest option to the correct equation is the one that uses the provided a and b values in the correct places.
Re-evaluating the Options Since none of the options perfectly match the derived equation y = − 3.1 x + 12.9 , let's re-examine the options and identify the one that most closely represents the line of best fit based on the given linear regression results. Option A is incorrect as it equates the correlation coefficient to the equation. Option B incorrectly uses the correlation coefficient as the slope. Option C swaps the values of a and b. However, if we consider the standard form y = a x + b , and we are given a = − 3.1 and b = 12.9 , the correct equation should be y = − 3.1 x + 12.9 . Among the given options, none is correct. However, if we were to choose the closest one, it would be the one that resembles the correct form.
Final Answer Given the options, we need to choose the one that represents the line of best fit, which is in the form y = a x + b . We know that a = − 3.1 and b = 12.9 . Therefore, the equation should be y = − 3.1 x + 12.9 . None of the options match this exactly. However, we can infer that there might be a typo in the options. Since the question asks for the line of best fit based on the given linear regression results, we should choose the option that uses the values closest to the calculated equation.
Conclusion Since none of the provided options perfectly match the line of best fit y = − 3.1 x + 12.9 , and there seems to be an error in the options, we cannot definitively choose one. However, if we had to select the closest one based on the given information, it would be the equation that uses the provided a and b values correctly. Since none of the options do that, we cannot provide a correct answer from the given choices.
Examples
Linear regression is used to model the relationship between two variables. For example, a company might use linear regression to model the relationship between advertising spending and sales revenue. The line of best fit can then be used to predict sales revenue for a given level of advertising spending. Understanding the equation of the line of best fit is crucial for making accurate predictions and informed business decisions. This helps in resource allocation and strategic planning by providing a quantitative basis for forecasting outcomes.
