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- Engro group, who recently sold its Engro foods start-up for a multi-million-rupees sum, islooking for another investment for fresh capital. It is considering an investment in coal (X) andsolar (Y) power plant. For that they had a collected data on 5 different characteristics. Amandahas applied k-means clustering to this data for k = 2. Given the following data:Table 5.1 Observations X Y 1 20 18 2 8 20 3 36 26 4 22 12 5 14 4 a) Which value of k is the most appropriate to categorize these investments? Justify yourchoice with calculations.b) The two cluster centers after the first round of execution. c) The final two clusters. d) Visually represent the clusters of both parts (b) and (c).Engro group, who recently sold its Engro foods start-up for a multi-million-rupees sum, is looking for another investment for fresh capital. It is considering an investment in coal (X) and solar (Y) power plant. For that they had a collected data on 5 different characteristics. Amanda has applied k-means clustering to this data for k = 2. Given the following data: Table 5.1 Observations X Y 1 20 18 2 8 20 3 36 26 4 22 12 5 14 4 Visually represent the clusters of both partsConstruction costs in East LA is not cheap. You want to build a simple cost estimator for construction costs, and you hope to find a useful linear relationship between cost (y) and floor space (x). You have data from a sample of four recently completed building projects: A. Since stat is not outside the critical values of ‡4.303, we can't reject the B=0 null hypothesis. B. Since stat is not outside the critical values of +2.182, we can't reject the B=0 null hypothesis C. Since stat is outside the critical values of ‡4.362, we can reject the B=0 null hypothesis. D. Since tstat is outside the critical values of +_3.182, we can reject the B=0 null hypothesis
- The management of BCD Inc. would like to separate the fixed and variable components of electricity as measured against machine hours in one of its plants. Data collected over the most recent six months follow:Electricity MachineMonth Cost Hours January $1,100 4,500February 1,110 4,700March 1,050 4,100April 1,200 5,000May 1,060 4,000June 1,120 4,600Required: 1. Using the method of least squares, compute the fixed cost and the variable cost rate for electricity expense. (Round estimates to the nearest cent.) 2. Compute coefficients of correlation and determinationSystematic variability occurs when: A. there are too many control variables B. there is a lot of variability in the data C. there is a design confound D. there are too many dependent variableAn agronomist undertook an experiment to investigate the factors that potato harvest. In his research, agronomist decided to divide the farm into 30 half hectare plots and apply varies level of fertilizer. Potato was then planted and the harvest at the end of the season was recorded. Fertilizer(Kg) Harvest (tons) 210 43.5 220 40.0 230 48.0 240 65.0 250 80.0 260 85.0 270 95.0 280 80.0 290 97.3 Note: No excel ANOVA output allowed. Students need to show all the steps in calculations. You are required to; Find the simple regression line and interpret the coefficients. Find the coefficient of determination and interpret its value. Does the model appear to be a useful tool in predicting the potato harvest? If so, predict the harvest when 250KG of fertilizer is applied. If not explain why not.
- An economist was interested in the relation between the disposable income of a family and the amount of money used for food per month. He did a preliminary study on eight randomly selected lower income families. (Each family was of the same size; father, mother and two children). The economist’s data are given in the table below. Food cost (Y) (in hundreds of rand) 55 60 42 40 37 26 39 43 Family disposable income(X) (in hundreds of rand) 30 36 27 20 16 24 19 25 Find the regression linear equation. What is the predicted food cost if the family disposable income is R1800 Find the correlation coefficient & Interpret r. Find the Coefficient of Determination & Interpret the R2.Neurosurgery Operative Times. An Arizona State University professor, R. Jacobowitz, Ph.D., in consultation with G. Vishteh, M.D., and other neurosurgeons obtained data on operative times, in minutes, for both a dynamic system (Z-plate) and a static system (ALPS plate). They wanted to perform a hypothesis test to decide whether the mean operative time is less with the dynamic system than with the static system. a. identify the variable. b. identify the two populations. c. determine the null and alternative hypotheses. d. classify the hypothesis test as two tailed, left tailed, or right tailed.Q: A large policy debate revolves about the causes and consequences of child labour. Extensive child labour at early ages is often considered as harmful and there is substantial theoretical and empirical interest in determining the causes for child labour. Therefore, we would like to analyze the relationship between wealth (e.g. the number of cattle or other assets) and child labour, using household data collected in several villages in rural Africa. Suppose we have data on Y and X iv where Y, is the number of hours worked by child i in village v and X, is family wealth. a) Explain how this is related to the concept of Panel Data. b) Explain how you could estimate the relationship between wealth and child labour using pooled OLS, Random Effect (RE), Fixed Effect (FE) estimators. Write down the estimation equations and the conditions needed to guarantee consistency. Compare the FE and the OLS estimators: Is either of these two estimators based on weaker assumptions than the other? c)…
- Site image for background. Conduct a test of the null hypothesis H0: u1=u2=u3=u4=u5 by stating (i) a test statistic value, (ii) an associate p-value, (iii) a decision at the a = 0.05 level, and (iv) a conclusion formulated in terms of Ha here for feed rate groups.What can we conclude from the fact that class size is negatively associated with the average grade in a college algebra course? A. Increasing the class size causes worse grades overall in a college algebra course B. College Algebra classes with larger class sizes typically (but not always) have a lower average grade. C. Reducing class size will increase grades in college algebra courses.Crop rotation is the practice of planting dissimilar crops sequentially in one locationto avoid the depletion of nutrients. A researcher conducted an experiment withsoybeans: they used crop rotation on 15 plots and left another 15 with no rotation. i. The researcher attaches particular importance to the reliability of theharvest as well as the actual harvest. Set out two descriptive statisticsthat could be useful to capture reliability. ii. Below are the number of pounds of soybeans harvested from each plot.Draw a boxplot to explain the data and explore any differencesbetween the two plots. (Do not carry out formal tests or confidenceintervals.) Crop rotation: 37, 42, 44, 46, 41, 39, 29, 31, 37, 41, 42, 45, 38 , 42, 33 No rotation: 29, 35, 34, 27, 31, 36, 41, 40, 37, 29, 31, 36, 24, 23, 22
