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Decisions Through Data Home


Statistics: Decisions Through Data

UNIT 9: Straight-Line Growth

Summary of the Video

The opening teaser sets growth as the topic. After introducing of the content to be presented, we look at human growth, which is close to linear after early infancy until adolescence. Sarah is growing slowly: a plot against time of her height shows a roughly linear pattern. Real data will rarely lie exactly on a straight line, so the line here just describes the overall pattern of the relationship. The slope of the line for Sarah's growth is smaller than normal, indicating a slow rate of growth. In Sarah's case, the cause is a deficiency of growth hormone. Regular injections of hormone increase her growth rate, as shown by a change in the slope of the line that describes her pattern of growth.

To discuss fitting lines to data in more detail, we switch to an artificial example: ticket sales to a movie in the weeks after its release. The sales are close to linear, but no line goes exactly through the points. We can fit a line to describe the pattern, either by eye or by using statistical software. (Unit 12 will describe the least-squares method, the most common way of fitting a line to data.) The equation of a line, y = mx + b, is more useful than a line drawn on the plot. Graphics on the screen review slope and intercept and how to plot a line given its equation.

Why fit a line to data? Prediction is one important reason. We can predict y for a given x on the graph (go up and over) or by substituting the given x into the equation. Few sets of real data are described by a straight line for all values of x, so in predicting we must beware of extrapolation. For example, predicting movie ticket sales eight years after release from data on the first few weeks gives a silly result.