Define the meaning of outliers. (a) (b) Explain THREE (3) tests for outlier detection in regression analysis. Identify the outliers for data in Table Q4(c) by constructing a box and whisker plot and plot the data set. (c) Table Q4(c) 30 21.4 39.4 33.4 21.1 29.3 32.8 31.6 36 27.9 27.3 29.4 29.1 38.6 33.8 29.1 37.1
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- With regard to regression, which of the following statements about outliers are true? I. Outliers have large residuals. II. A point may not be an INFLUENTIALoutlier even though its x-value is an outlier in the x-variable and its y-value is an outlier in the y-variable. III. Removal of an outlier sharply affects the regression line. II and III I, II, and III I and II I and III I only ( don't hand writing solution)A university would like to examine the linear relationship between a faculty member's performance rating (measured on a scale of 1-20) and his or her annual salary increase. The table to the right shows these data for eight randomly selected faculty members. Complete parts a and b.1. Amanda Boleyn, an entrepreneur who recently sold her start-up for a multi-million-dollar sum, is looking for alternate investments for her newfound fortune. She is considering an investment in wine, similar to how some people invest in rare coins and fine art. To educate herself on the properties of fine wine, she has collected data on 13 different characteristics of 178 wines. Amanda has applied k-means clustering to this data for k = 1, ... , 10 and generated the following plot of total sums of squared deviations. After analyzing this plot, Amanda generates summaries for k = 2, 3, and 4. Which value of k is the most appropriate to categorize these wines? Justify your choice with calculations. Answer the following: Do not round intermediate calculations. If required, round your answers to two decimal places. k = Cluster 1 to Cluster 2 Distance / Cluster 1 Average Distance = Cluster 2 to Cluster 1 Distance / Cluster 2 Average Distance = Average = k = 3Cluster 1…
- An auctioneer of antique Iranian rugs kept records of his weekly auctions in order to determine the relationships among price, age of carpet or rug, number of people attending the auction, and the number of times the winning bidder had previously attended his auctions. He felt that, with this information, he could plan his auctions better, serve his steady customers better, and make a higher overall profit for himself. The results shown in the accompanying table were obtained.In a study of the stability of IQ scores, a large group of individuals is tested once at age 18 and again at age 35. The following results are obtained. At age 18: average score = 100, SD = 10At age 35: average score = 100, SD = 10 The correlation coefficient between scores at age 18 and 35 is 0.60 and the scatter plot is football shaped. What percent of the individuals with a score of 120 at age 18 score more than 100 at age 35?Ten corvettes between 1 and 6 years old were randomly selected from the classified ads of The Arizona Republic. The following data were obtained, where x denotes age, in years, and y denotes price, in hundreds of dollars. X (age) 6 6 6 2 2 5 4 5 1 4 Price (100ths) 270 260 275 405 364 295 335 308 405 305 Does a linear relationship exist between the age of a corvette and its price? (use the critical value to explain)If appropriate, explain the slope in context.If appropriate, explain the y-intercept in context.Predict the price of a one-year-old corvette.Find the Residual of a one-year-old corvette
- Mumbai Electronics is planning to extend its marketing region from the western United States to include the midwestern states. In order to predict its sales in this new region, the company has asked you to develop a linear regression of DVD system sales on price, using the following data supplied by the marketing department: Sales 418 384 343 407 432 386 444 427 Price 98 194 231 207 89 255 149 195 a. Use an unbiased estimation procedure to find an estimate of the variance of the error terms in the population regression. b. Use an unbiased estimation procedure to find an estimate of the variance of the least squares estimator of the slope of the population regression line. c. Find a 90% confidence interval for the slope of the population regression line.A researcher desires to know if the age of a child is related to the number of cavities he or she has. The data is below. Age of child, x 6 8 9 10 12 14 No. of cavities, y 2 1 3 4 6 5 Perform a hypothesis test to determine if there is a linear relationship between the variables. Find the coefficient of determination and interpret it Using s, determine if there are any outliers.A manufacturing company is interested in predicting the number of defects that will be produced each hour on the assembly line. The managers believe that there is a relationship between the defect rate and the production rate per hour. The managers believe that they can use production rate to predict the number of defects. The following data were collected for 10 randomly selected hours. Defects (Y) Production rate per hour(X) 2 40 3 45 1 35 2 37 3 40 2 40 3 45 2 30 1 30 4 30 (a). Construct a scatter plot diagram and comment on the relationship between y and x (b). Calculate the correlation coefficient (r) between x and y and comment on the result. (c). Find the coefficient of determination and interpret the result.
- A sample correlation r = 0.60 indicates a stronger linear relationship than r = 0.40. True FalseThree landmarks of baseball achievement are Ty Cobb's batting average of 0.420 in 1911, Ted Williams' 0.406 in 1941, and George Brett's 0.390 in 1980. These batting averages cannot be compared directly because the distribution of major league batting averages has changed over the years. The distributions are quite symmetric and, except for outliers such as Cobb, Williams, and Brett, reasonably Normal. While the mean batting average has been held roughly constant by rule changes and the balance between hitting and pitching, the standard deviation has dropped over time. Here are the facts: Decade Mean Std. dev. 1910s 0.266 0.0371 1940s 0.267 0.0326 1970s 0.261 0.0317 Compute the standard scores for the batting averages of Cobb, Williams, and Brett to compare how far each stood above his peers. Enter your answers to two decimal places. Ty Cobb's standard score: Ted Williams' standard score: George Brett's standard score:Given the following data on lawnmower engine emissions and age of the lawnmower Age Emission 0 1.72 0 4.38 2 4.06 11 1.26 7 5.31 16 0.57 9 3.37 0 3.44 12 0.74 4 1.24 Construct a scatterplot of emissions versus age What are the characteristics of the scatter plot? Do age and emission appear to be related?