Once again all examples below are found on the Examples Workbook. We will look at 2 techniques, one built-in to Excel called Charts and another which is a User Defined Function (UDF) I developed.īoth techniques have uses in analysis of trends. In todays final post of Are You Trendy? we will take a break from the maths and discuss techniques and tools that Excel provides to assist us with Trend Analysis. It's quite possible that he started the race at the starting line but the model needed to have a y-intercept of 10 to attain the least error between the model and the actual data over the entire data set.So you’ve made it to part 3 of Are You Trendy, well done. For example, the line that represents Ray's distance from the starting line indicates that he started the race 10 meters ahead of the starting line. The equation that is created when you perform linear regression is an equation for the linear model that produces the least amount of error between the actual output values ( y-values) in the data set and the output values predicted by the model for those input values ( x-values).īecause the line only approximates the data, many of the data points may not lie on the line and the model may imply erroneous conclusions. Below are the graphs for the two runners in a x Viewing window.Ģ.3.4 What do the slopes tell you about the two runners? What do the y-intercepts tell you about the start of the race? Who won? Click here for the answer. The corresponding equation for Ray is y = 8.1 x + 10.
Carl's distance from the starting line after the start of the race can be modeled by y = 10.7 x, where x represents time in seconds and y is measured in meters. Where x is the size in square feet and y is the price of the house.Ģ.3.3 What does the slope of this line tell you about the homes listed in this area? What does the y-intercept tell you? Click here for the answer.Ĭarl and Ray compete in a 100-meter dash. The scatter plot for the data looked approximately linear and the linear regression equation for the data was found to be The real estate section of a local newspaper listed the selling price along with the size in square feet for houses that are for sale in the area. What does the slope of this line tell you about the value of an average house in this area? What does the y- intercept tell you? Click here for the answer. Is more descriptive than just stating that the slope is -1478.Ģ.3.2 The linear equation that describes the value of an average home is y = 5632 x + 14760, where x is years since 1970 and y is the value of an average house in dollars. In the previous example, stating the slope as X will help clarify what the slope tells you about how the y-value changes from one x-value to the next. Y (read "delta y"), divided by the change in x, The slope of the line that best fits the car data is -1478 dollars per year and the y-intercept is 13,906 dollars.Ģ.3.1 What does the slope of the line of best fit tell you about the change in the value of this model of car? What does the y-intercept tell you about the value of the car? Click here for the answer. Where x represents the age of the car and y represents the car's value. Recall that the line of best fit for the car values found in Lesson 2.2 was The y-intercept indicates the y-value when the x-value is 0. The slope indicates the rate of change in y per unit change in x. The slope and y-intercept values indicate characteristics of the relationship between the two variables x and y. If any point on this line is used to write a point-slope form for the equation, it will simplify to the same slope-intercept form. Even though the point-slope forms appear different, the slope-intercept forms are identical. Notice that both equations are transformed into the same slope-intercept equation. The equations wereĮach equation can be changed into slope-intercept form by performing the indicated multiplication and combining the constant terms. In Lesson 2.1 you found two point-slope equations that represent the line through the points (-1, -2) and (2, 3). This form of a linear equation is called the "slope-intercept" form of a line.Ĭhanging Point-Slope Form to Slope-Intercept Form Where m is the slope of the line and b is the y-intercept. This lesson explores the meaning of slope and y-intercept in the context of the car-value problem that was introduced in Lesson 2.2.Īny non-vertical line can be written in the form The slope and y-intercept of the best-fit line are helpful in understanding a set of data and the relationship that exists between the quantities in the set. Module 2 - Lines - Lesson 3 Module 2 - Lines