Regression Lines and Scatter Plots 1. Scatter Plots: Scatter plots are used search for possible relationships between two variables; the Explanatory Variable is always on the horizontal axis (x-axis) and the Response Variable is always on the vertical axis (y-axis). For example, you might think there is a relationship between the quantity of frozen diet means consumed per week by an individual and that person's body mass index (BMI). The following scatterplot was created by surveying 60 people between the ages of 18 to 35. Each person was asked "How many frozen meals do you each per week?" and each of their BMI's were reported. Use the scatter plot to answer the following questions. (a) What is the Explanatory Variable and the Response Variable in this scatter plot? (b) We want to describe the overall pattern between of the relationship between these two variables (using direction, form, and strength) and striking deviations (if any) from the overall pattern. First What is the direction of your scatterplot positive (increasing), negative (decreasing). or neither? (c) What overall form does the data in your scatterplot have (linear or curvilinear if you don't know what these are ask the teacher]? (d) Guesstimate the strength of the relationship of the data in your scatterplot (for now. . . weak, fairly strong, strong, or very strong). Explain your choice. (e) Are there any striking deviations from the overall pattern (a.ka. outliers)?2. These scatterplots show various body measurements for 34 adults who exercise several times each week. De- scribe the overall pattern with regard to direction, form, and strength. Then describe any striking deviations from the pattern. Softerplet I Scatterplot 2 Srafterplot 3. For each scatterplot, describe the overall pattern of the relationship between the two variables (using direction, form, and strength) and striking deviations (outliers) from the overall pattern. Scatterplot 4 Scatterplot 5 Scatterplot 5 Scatterplot 7 Scatterplot 8 Scatterplot 94. Correlation Coecient: The correlation coecient r is a numerical value ranging from 1 to 1 derived from bivariant data (the data from exploratory and response variables.) It helps describe the strength and direction of the relationship between the two variables in a single numerical value. If r is positive, the overall trend of the data is increasing. If r is negative, then the overall trend of the data is decreasing. If the r is really close to 0, then the dots look scattered or do not really collect around a line (the relationship is weak). If r is closer to 1 or 1, then the dots have a stronger relationship to a line. For each of the following scatterplots match the listed correlation coecients; reOr=05r=05r = 0.75r = 0.75r=0.9r=0.9r=1r=15. Best fit line, Regression Line, Least Square Line: We would like to be able to make prediction from the scatterplot data. One way to do this is create a" best fit line". Then use the line to predict values that have not been measured yet. Let's label our variables; x is the explanatory variable. y is the response variable. y is the predicted response variable that we get by using our best fit line. In general, the formula we use in statistics for the best fit line is y=a+bx where a and b found from the bivariant data and are constants. In this case b is the rate of change, or slope of the line and a is the initial value or y-intercept of the line. Below we have data from 21 college students. Forearm length in inches is the explanatory variable. Height in inches is the response variable. The line is a good summary of the linear pattern in the data. Height (inches] RO 85 20 95 100 105 11.0 115 120 125 Forearm (ickes) The equation of the line is given by the following regression equation. Predicted height = 39 + 2.7 . forearm length (a] Based on the graph of this line, which is the best prediction of the height of a woman with a forearm of 11 inches? A. 64.5 inches B. 68 inches C. 68.75 inches D. just under 72 inches (b) What is the most precise and accurate interpretation of the slope? (c) Use the equation of the line to predict the height of a woman with a 10-inch forearm. Show your work