Residuals in a regression model: (pick one or more) * A) Represent the differences between observed values and values predicted by a regression model * B) smaller (in absolute value) in a poorly fitted compared to a fitted model * C) Contribute to the calculation of an F test statistic

Observations are taken on sales of a certain mountain bike in 30 sporting goods stores. The regression model was Y= total sales (thousands of dollars), X₁ = display floor space (square meters). X₂ competitors' advertising expenditures (thousands of dollars), X3 = advertised price (dollars per unit). Predictor Intercept FloorSpace Competing Ads Price Coefficient 1,287.26 11.52 -6.934 -0.1476 (a) Write the fitted regression equation. (Round your coefficient Competing Ads to 3 decimal places, coefficient Price to 4 decimal places, and other values to 2 decimal places. Negative values should be indicated by a minus sign.) ý= 1,287 26 + 11:52 *FloorSpace + (6.934) CompetingAds + (0.1446) * Price

Data on 12 randomly selected athletes was obtained concerning their cardiovascular fitness (measured by time to exhaustion running on a treadmill) and performance in a 20-km ski race. Both variables were measured in minutes and a regression analysis was performed. ski 85 2.5. treadmill = Coefficients Estimate (Intercept) Treadmill 85 - 2.5 Std. Error What is the test statistic? -2.5 0.45 1 Is there sufficient evidence to conclude that there is a linear relationship between cardiovascular fitness and ski race performance? Round your answers to three decimal places. Using your answer from the previous question, find the p-value. Part 2 o

We were comparing two varibles (male and female math score)by linear regression which gives us a residual plot   question   1.What is/are the purpose(s) of a residual plot in regression analysis? For the residual plot drawn in part (d), explain what you learn in the context of this problem   2.What is the purpose of drawing a histogram of the residuals in regression analysis? For the histogram of residuals drawn in part (f), explain what you learn in the context of this problem.(histogram for residuals)   my answer for 1-The residual plot is to ensure or check a linear regression model is appropriate. In our case, data points are evenly placed on two sides of horizontal axis, so it is appropriate.   for 2 does that tells us the data is normally distributed or not? what does the graph tells us. does the U shape means normally distributed? ( I know it is if its symmetric hill shape).