Which assumption of a linear regression model appears to be violated based on the following plot of the model residuals versus the fitted values?
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- Olympic Pole Vault The graph in Figure 7 indicates that in recent years the winning Olympic men’s pole vault height has fallen below the value predicted by the regression line in Example 2. This might have occurred because when the pole vault was a new event there was much room for improvement in vaulters’ performances, whereas now even the best training can produce only incremental advances. Let’s see whether concentrating on more recent results gives a better predictor of future records. (a) Use the data in Table 2 (page 176) to complete the table of winning pole vault heights shown in the margin. (Note that we are using x=0 to correspond to the year 1972, where this restricted data set begins.) (b) Find the regression line for the data in part ‚(a). (c) Plot the data and the regression line on the same axes. Does the regression line seem to provide a good model for the data? (d) What does the regression line predict as the winning pole vault height for the 2012 Olympics? Compare this predicted value to the actual 2012 winning height of 5.97 m, as described on page 177. Has this new regression line provided a better prediction than the line in Example 2?Life Expectancy The following table shows the average life expectancy, in years, of a child born in the given year42 Life expectancy 2005 77.6 2007 78.1 2009 78.5 2011 78.7 2013 78.8 a. Find the equation of the regression line, and explain the meaning of its slope. b. Plot the data points and the regression line. c. Explain in practical terms the meaning of the slope of the regression line. d. Based on the trend of the regression line, what do you predict as the life expectancy of a child born in 2019? e. Based on the trend of the regression line, what do you predict as the life expectancy of a child born in 1580?2300The following result perspective in RapidMiner shows a multiple linear regression model. Based on the diagram, the model for our dependent variable Y is Predicted Y= (Insulation *0.420)+(Temperature *0.071)+(Avg_Age*0.065)+(Home_Size *0.311)+7.589 Attribute Insulation Temperature Avg Age Home Size (Intercept) O True O False Coefficient 3.323 -0.869 1.968 3.173 134.511 Std. Error 0.420 0.071 0.065 0.311 7.589 Std. Coefficient 0.164 -0.262 0.527 0.131 ? Tolerance 0.431 0.405 0.491 0.914 ? t-Stat 7.906 -12.222 30.217 10.210 17.725
- Which of the variables is the indepenent variable and dependent variable for the following question. fit a simple linear regression model to predict latitudes using average monthly range lat= latitudes range= the average monthly range between mean montly maximum and minimum temperatures for a selected set of US cities.please do all parts! The estimated regression equation for this data set is y=4.4878+1.9549x. Part A: (in image) Part B: is the linear function is the appropriate regression function for this data set? Part C: do the residuals have a constant variance? Part D: are the residuals independent? Part E: are the error terms are normally distributed? y x22 821 818 846 2241 2254 2276 3258 3268 32Which is an assumption of linear regression analysis? The mean of the residuals should be
- Online clothes II For the online clothing retailer dis-cussed in the previous problem, the scatterplot of Total Yearly Purchases by Income showsThe correlation between Total Yearly Purchases and Incomeis 0.722. Summary statistics for the two variables are: a) What is the linear regression equation for predictingTotal Yearly Purchase from Income? b) Do the assumptions and conditions for regression ap-pear to be met? c) What is the predicted average Total Yearly Purchasefor someone with a yearly Income of $20,000? Forsomeone with an annual Income of $80,000?d) What percent of the variability in Total YearlyPurchases is accounted for by this model?e) Do you think the regression might be a useful one forthe company? Comment.A sample consists of 500 houses sold in Karachi between Jamuary 2020 and December 2020. The multiple linear regression analysis is carried out to predict the house prices for investment in residential properties in Karachi, Pakistan. The output below is produced using SPSS. (300 words) Table: Coefficients Model Unstandardized Coefficients VIF Constant 14.208 5.736 Age of house -0.299 -2.322 1.58 Square footage of the house 0.364 2.931 1.71 Income of families in the area p.004 0.392 1.01 Transportation time to major markets -0.337 -2.619 1.90 R? = 0.67; DW = 2.08 Dependent Variable: House price (Pakistani rupees in Million) a) You are required to write the multiple regression equation. b) How would you interpret the above Output' of a regression analysis performed in SPSS? c) From the above results, what can you say about the nature of autocorrelation? d) Is there multicollinearity in regression? How do you know?Aboxplot of the residuals and a scatterplot of the residuals versus the predicted values are provided. Discuss whether the conditions for a multiple linear regression are reasonable by referring to the appropriate plots. Residual Residual 25 50 5 25 8 200 300 500 600 Predicted Calories 400 700 No-Even though the boxplot is roughly symmetric and there are no outliers, the scatterplot of the residuals versus the predicted values shows inconsistent variability Yes-The boxplot is roughly symmetric and there are no outliers. The scatterplot of the residuals versus the predicted values is fairly scattered No curved patterns are apparent No The boxplot showes that the distribution of residuals is not perfectly symmetrical No Even though the boxplot is roughly symmetric and there are no outliers, the scatterplot of the residuals versus the predicted values shows curvatures and fanning patterns are apparent
