b₁₁ = 20 b=C+DtP3 b₁₂ = b3=8 e2 P2 1 P1 e1 b₁₁ = 0 4₁=0 12 = 1 eA PA b = (0,8,8,20) p = Ca₁ + Da2 a2 = (0, 1, 3, 4) 2 a₁ = (1, 1, 1, 1) 13 = 3 14=4 Figure 4.9: Problems 1-11: The closest line C + Dt matches Ca₁ + Da₂ in R4. With b = ΑΤΑΞ 0,8,8,20 at t = 0,1,3,4, set up and solve the normal equations ATb. For the best straight line in Figure 4.9a, find its four heights pi and four errors e¿. What is the minimum value E = e² + e² + e² + e²? =
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- 2. Suppose that in Example 2.27, 400 units of food A, 500 units of B, and 600 units of C are placed in the test tube each day and the data on daily food consumption by the bacteria (in units per day) are as shown in Table 2.7. How many bacteria of each strain can coexist in the test tube and consume all of the food? Table 2.7 Bacteria Strain I Bacteria Strain II Bacteria Strain III Food A 1 2 0 Food B 2 1 3 Food C 1 1 1Q4.2 1-17/18Suppose that your friend sees the results from question 4 and concludes that heavier drinking causes more tobacco use. Do you agree or disagree with this conclusion? Explain.
- FORMULATE A PROBLEM OUT OF THIS DATA. THANK YOUOnly b.ii, iii and iv please. The output of a solar panel (photovoltaic) system depends on its size. A manufacturer states that the average daily production of its 1.5 kW system is 6.6 kilowatt hours (kWh) for Perth conditions. A consumer group monitored this 1.5 kW system in 20 different Perth homes and measured the average daily production by the systems in these homes over a one month period during October. The data is provided here. (a) Analyse the consumer group’s data to test if the manufacturer’s claim of an average of 6.6 kWh per day is reasonable. State appropriate hypotheses, assumptions and decision rule at α = 0.10. What conclusions would you report to the consumer group? Hint: You will need to find Descriptive Statistics first.) (b) If 48 homes in the central Australian city of Alice Springs had this system installed and similar data wascollected, in order to assess whether average daily production in Alice Springs exceeded 6.6 kWh, (i) what would the alternate hypothesis…Problem: Four groups of 4 patients @ were subjected to 4 different types of treatment for the same ailment. The following data are on the number of days that elapsed before they were completely cured. What conclusions may be drawn about the 4 types of treatment? (F cri = 3.49, level of significant = 0.05) Patient 1 2 3 4 Treatment A 10 9 6 7 Treatment B 11 11 18 6 Treatment C 3 4 457 7 Treatment D 6 10 8 11
- (2) Sdr= 1 x=. V1-x2State the type of variable in each of the following cases 1- 5.1. The weight (Kg) of an Amazon package.2. The stress level (Low, Average, High) of a student taking this exam.3. The number of Long Covid-19 patients in England in 2021.4. Type of vaccine (Pfizer, AstraZeneca, Moderna).5. The annual profits (£m) of the JSA company in 2021.Your answer should be A, or B or C or D, where A, B, C, and D are defined asfollows:A. Numerical and DiscreteB. Numerical and ContinuousC. Categorical and NominalD. Categorical and Ordinal(d) Figure 2.85(a) shows the same scatterplot with a third variable included. Is the new variable categorical or quantitative? If categorical, how many categories? If quantitative, estimate the range. e) In Figure 2.85(a), if we only consider cases in Group A, does the association between Variable1 and Variable2 appear to be positive or negative? How about in Group B? Group C? Group D? (f) Figure 2.85(b) shows the same scatterplot as Figure 2.85(a) with regression lines added within each of the four groups. Does the regression line for Group A show a positive or negative association? How about Group B? Group C? Group D? (g) What happens to the direction of association shown in Figure 2.84 when we add the additional information contained in Variable3 as in Figure 2.85? (This is an example of Simpson's Paradox for quantitative variables.)
- 9.3 cannot use a calculator like a TI-89 or a TI-nSprire CA way please1. (10 ) According to the PayScale data from 2021, the average starting salaries by college major for bachelor's degree are as follows: $70,600 for mechanical engineering, $56,700 for economics, $43,500 for chemistry, and $47,000 for philosophy. In order to estimate the true difference in the average starting salaries by college major in 2022, 60 graduates with these four majors from the class of 2022 were contacted and questioned about their starting salaries. Propose a regression model with dummy variables that could be used to investigate if starting salaries are different by college major and interpret all the coefficients in the model. 0.000Otitis media is a disease that occurs frequently in the firstfew years of life and is one of the most common reasonsfor physician visits after the routine checkup. A study wasconducted to assess the frequency of otitis media in thegeneral population in the first year of life. Table 4.15 givesthe number of infants of 2500 infants who were first seen atbirth who remained disease-free by the end of the ith monthof life, i = 0, 1, . . . , 12. (Assume no infants have been lostto follow-up.) Disease-free infants ati the end of month i0 25001 24252 23753 23004 21805 20006 18757 17008 15009 130010 125011 122512 1200 Suppose an “otitis-prone family” is defined asone in which at least three siblings of five develop otitis media in the first 6 months of life. What proportionof five-sibling families is otitis prone if we assume thedisease occurs independently for different siblings in afamily?