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How to Use Trend Lines and Predictions for Homework Practice: Lesson 2 Answer Key



Lesson 2 Homework Practice Use Trend Lines To Make Predictions Answer Key




In this article, you will learn how to use trend lines to make predictions based on data. Trend lines are one of the most popular price action indicators in the technical analysis of stocks, currency pairs, and cryptocurrencies. One can draw trend lines by joining a series of prices representing a financial instrument s support and resistance in any duration.




Lesson 2 Homework Practice Use Trend Lines To Make Predictions Answer Key



Introduction




What are trend lines and why are they useful for data analysis? How to draw trend lines on a scatter plot and find their equation? How to use trend lines to make predictions based on data?


These are some of the questions that you may have when you encounter trend lines in your homework or in real-life situations. In this article, we will answer these questions and show you how to apply trend lines to various examples.


Trend Lines: Definition and Purpose




Trend lines are straight lines that connect two or more points on a graph and show the general direction of the data. Trend lines can be used to identify patterns, trends, and relationships among variables. Trend lines can also be used to estimate values of one variable based on another variable.


For example, suppose you have a scatter plot that shows the height and weight of different dogs. You can draw a trend line that shows how weight changes as height increases. This trend line can help you see if there is a positive or negative correlation between height and weight, and how strong or weak it is. It can also help you estimate the weight of a dog that has a certain height, or vice versa.


Drawing Trend Lines and Finding Their Equation




To draw a trend line on a scatter plot, choose two points that lie close to most of the data points and draw a line through them. You can use a ruler or a software tool to make the line as straight as possible. The two points that you choose are called the anchor points of the trend line.


To find the equation of a trend line, use the slope-intercept form: y = mx + b, where m is the slope and b is the y-intercept. The slope is the rate of change of y with respect to x, or how much y increases or decreases as x increases by one unit. The y-intercept is the value of y when x is zero, or where the line crosses the y-axis.


To find the slope, use the formula: m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are any two points on the line. You can use the anchor points or any other points that lie on the line.


To find the y-intercept, plug in the values of x and y for any point on the line and solve for b. You can use the anchor points or any other points that lie on the line.


For example, suppose you have a scatter plot that shows the relationship between hours of study and test scores for some students. You draw a trend line that passes through the points (2, 70) and (6, 90). To find the equation of this trend line, follow these steps:



  • Find the slope: m = (y2 - y1) / (x2 - x1) = (90 - 70) / (6 - 2) = 20 / 4 = 5



  • Find the y-intercept: plug in x = 2 and y = 70 into y = mx + b and solve for b: 70 = 5(2) + b -> b = 70 - 10 -> b = 60



  • Write the equation: y = mx + b -> y = 5x + 60



The equation of this trend line is y = 5x + 60. This means that for every hour of study, the test score increases by 5 points, and when no hours are spent studying, the test score is 60.


Using Trend Lines to Make Predictions




= 60 and solve for y using the equation of the line. For example, if the equation of the trend line is y = 0.5x + 10, then y = 0.5(60) + 10 = 40. This means that a dog that is 60 cm tall is predicted to weigh 40 kg.


The predicted value of y is called the y-hat or the estimated value of y. It is denoted by a symbol that looks like a y with a hat on top: ŷ. The difference between the actual value of y and the predicted value of y is called the residual or the error. It is denoted by a symbol that looks like an e: e. The formula for the residual is: e = y - ŷ.


For example, suppose you have a dog that is 50 cm tall and weighs 25 kg. You want to compare its weight to the predicted weight based on the trend line. If the equation of the trend line is y = 0.5x + 10, then ŷ = 0.5(50) + 10 = 35. This means that a dog that is 50 cm tall is predicted to weigh 35 kg. The residual is: e = y - ŷ = 25 - 35 = -10. This means that the actual weight of the dog is 10 kg less than the predicted weight.


Conclusion




In this article, you learned how to use trend lines to make predictions based on data. Trend lines are useful tools for data analysis that can help you visualize patterns, trends, and relationships among variables.


To draw a trend line on a scatter plot, choose two points that lie close to most of the data points and draw a line through them. To find the equation of a trend line, use the slope-intercept form: y = mx + b, where m is the slope and b is the y-intercept.


To use a trend line to make predictions based on data, plug in the value of x or y that you want to predict and solve for the other variable using the equation of the line.


FAQs




  • Q: What are some examples of real-world situations where trend lines can be used?



  • A: Some examples are: predicting sales based on advertising spending, predicting life expectancy based on income level, predicting population growth based on birth rate, etc.



  • Q: How can you tell if a trend line is a good fit for the data?



  • A: One way to tell if a trend line is a good fit for the data is to look at how close most of the data points are to the line. The closer they are, the better the fit. Another way is to calculate the correlation coefficient (r), which measures how strong the linear relationship between two variables is. The closer r is to 1 or -1, the better the fit.



  • Q: What are some limitations of using trend lines for predictions?



  • A: Some limitations are: trend lines may not capture all the factors that affect the variables, trend lines may not account for outliers or extreme values that deviate from the pattern, trend lines may not work well for nonlinear or curved relationships, trend lines may not be valid for values outside the range of the data.



  • Q: How can you improve your trend line by using more than two points?



  • A: One way to improve your trend line by using more than two points is to use a method called linear regression, which finds the best-fitting line that minimizes the sum of squared errors between the actual and predicted values. Linear regression can be done using a calculator or a spreadsheet program.



  • Q: How can you extend your trend line beyond the range of your data?



  • A: One way to extend your trend line beyond the range of your data is to use extrapolation, which means making predictions based on extending or projecting the trend line. However, extrapolation can be risky, as it assumes that the trend will continue indefinitely, which may not be true in reality. Extrapolation should be done with caution and common sense.



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