Answer Happy

Correlation and Regression Lab Does Fidgeting Keep You Slim? Some people don't gain weight even when they overeat. Fidgeting and other non-exercise activities (NEA) may explain why. Researchers deliberately overfed 16 healthy young adults for 8 weeks. They measured fat gain and NEA change. The data is in Table 1. Table NEA Change (cal.) Fat Gain (kg.) NEA Change (cal.) Fat Gain (kg.) Who are the individuals? STAT PLOTS 1 Ploti...On 2: L2 1 Plot2...Off di L2 3: Plot3...Off 1 L1 4+PlotsOff L2 B -94 4.2 392 5.0 4. Are there any outliers? STAT 1350: Elementary Statistics -57 3.0 473 1.7 Yes -29 3.7 486 1.6 Plot1 Plotz Plot3 On Off Type: Xlist: L1 Ylist: Lz Mark: No Jel AN HHHH 135 2.7 535 2.2 What is the explanatory variable? We will use the TI Graphing calculator. Enter NEA change data (all 16 values) in L₁ and fat gain data (all 16 values) in L₂. Turn on PLOT1 and choose TYPE scatterplot (first selection). XLIST should be explanatory variable and YLIST should be response variable. 4 Linear Weak Name(s): 143 3.2 571 1.0 151 3.6 Response Variable? Use ZOOMSTAT. (ZOOM 9) to GRAPH. Use the scatterplot displayed to answer the following questions. Circle your answers: 1. What is the type (direction) of the relationship? Positive 2. What is the form of the relationship? 3. What is the strength of the relationship? Negative 580 0.4 Nonlinear Moderate 245 2.4 620 1.8 355 1.3 Strong 690 1.1 If yes, which point(s) represent possible outliers?
Our eyes can be fooled by how strong a linear relationship is; we need to use a numerical measure, correlation, or r to accurately describe the association between NEA and Fat Gain. Correlation measures the strength and direction (type) of linear relationships. The formula for correlation is: Correlation r= This is quite tedious to do by hand, so we will use our calculator to obtain the value of the correlation Using your calculator, press STAT, choose CALC, then 8:LinReg (a+bx). Enter Ls, La. Then press the ENTER key to get the correlation Does this value support your answer for question #3 on page 1? Explain why or why not When a scatterplot shows a linear relationship, we would like to summarize the overall pattern by drawing a line on the scatterplot. A regression line describes how a response variable changes as an explanatory variable changes. The least-squares regression line is the line that makes the sum of the squares of the vertical distances of the data points to the line as small as possible. (See figure 15.3 on p339 in text) The form of the equation of a line is y = a + bx where a is the y-intercept, the value of y when x=0, and b is the slope, the amount y changes when x increases by one unit. Using your calculator, press STAT, choose CALC, 8: LinReg (a+bx). Enter L₁, L2. Then press the ENTER key to get the coefficients for the least-squares regression line. The equation of the least-squares regression line is The square of the correlation, r², is the proportion of the variation in the values of y that is explained by the linear relationship with x. r² =
Use the least squares line, y = a + bx, to answer the following questions: 1. If a person had no change in their NEA, what would their fat gain/loss be? I What is this point called on the graph of the least-squares regression line? 2. If a person had 500 calorie NEA change, what would their fat gain/loss be? 3. What proportion of the variation in fat gain can be explained by the linear relationship with NEA change? 4. Should you use this regression line to predict fat gain for a NEA change of 1000 calories? Why or why not? 5. Outliers can affect the correlation between two variables. To see how the correlation can be affected by outliers, remove the person in the list whose NEA change was 392 calories and Fat Gain 5.0 kg. Now recalculate the value of the correlation (r). r= How did removing this person's data affect the strength of the correlation?