1. Use (11.20) to check whether the following functions are concave, convex, strictly con- cave, strictly convex, or neither: (a) z = x? (b) z = x}+ 2x3 (c) z= 2x2-xy + y? following functions are concave, convex.
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- a survey showed that 20 percent of the offereed meals to employees and 15 percent offered meals for the paid extras . which is greater quanity A : the percent that offered to their employees but not the paid extras quanity b: 16 percent.A student would like to know which establishment would allow him to save more money from everyday food costs. He is choosing between AVM or Hollywood Terraces, so he traced his spending in both establishments for 1 school week each, his data is as follows: AVM: 97, 85, 69, 105, 105 HT: 60, 45, 60, 75, 100 Find out if there is a significant difference in his spending between the two food courts.The management of a supermarket wants to find if there is a relationship between the number of times a specific product is promoted on the intercom system in the store(x) and the number of units of that product sold (y). To experiment, the management selected a product and promoted it on the intercom system for 7 days, recording the number of times this product was promoted each day and the number of units sold. Summaries of a study conducted gave the following results: ∑x=177, ∑y= 144, SSxx=809.4286, SSyy=261.7143, SSxy= 407.8571 a) Calculate the correlation coefficient (r) relating number of times this product was promoted each day and the number of units sold. b) Find the regression line.
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- Determine the best (according to sum-of-squares-measure) curve y = ax2 + bx + c, throughthe data above.Compute ? and find out if age (in years) has a relation to the blood pressure of an individualthe following data represent the operating time in hours fro 4 types of pocket calculators before a recharge is required. test at 0.01 level of significance if the operating times for all four calculators are equal. Find the following: MSbet: Mswit: Fratio: F0.01: Decision:
- In a recent survey, ice cream truck drivers in Cincinnati, Ohio, reported they make about $280 in income on a typical summer day. The income was generally higher on days with longer work hours, particularly hot day, and on holidays. The IceCream data file includes five weeks of the driver's daily income (Income), number of hours on the road (Hours), whether it was a particularly hot day (Hot = 1 if the high temperature was above 85-degrees F, 0 otherwise), and whether it was a Holiday (Holiday = 1, 0 otherwise). 1. Predict the income of a driver working 8 hours on a hot holiday. (Round to the nearest dollar.) 2. Predict the income of a driver working 8 hours on a hot day if it was not a holiday. (Round to the nearest dollar.)In this task, you can use all functions of R to help you. In a recently conducted study, it was tested whether there is a connection between job satisfaction and income and seniority in nine randomly selected employees. The value attached to job satisfaction is each employee's own assessment, where 1 describes low satisfaction and 10 high satisfaction. Material: annual income (per thousand dollars) years spent in job satisfaction 47 8 5.6 42 4 6.3 54 12 6.8 48 9 6.7 56 16 7.0 59 14 7.7 53 10 7.0 62 15 8.0 66 22 7.8 The result was the material below a) Fit a two-explainer linear regression model to the data with R's function lm(). What happens to job satisfaction as the number of years increases? For explanatory variables, can the null hypothesis that the corresponding regression coefficient is equal to zero be rejected? b) It is assumed that job satisfaction is only related to years in that job. Estimate the regression parameters using R software. What…William Profit is studying companies going public for the first time. He isparticularly interested in the relationship between the size of the offering and theprice per share. A sample of 15 companies that recently went public revealed the following information: y x 10.8 9 11.3 94.4 11.2 27.3 11.1 179.2 11.1 71.9 11.2 97.9 11 93.5 10.7 70 11.3 160.7 10.6 96.5 10.5 83 10.3 23.5 10.7 58.7 11 93.8 10.8 34.4