Fit a straight line trend by the method of least squares to the following data and ´predict the sales for 2001 : Year: 1994 1995 1996 1998 1999 1997 Sales (in '000=) 15 17 20 23 21 24
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- Compute the sum-of-squares error (SSE) by hand for the given set of data and linear model. (8, 10), (9, 11), (16, 20), (12, 2); y = 2x − 8The following table shows the percent of water and the number of calories in various canned soups to which 100 g of water are added. (show all the necessary solution) Percent Water in Soups % Water Calories 83.3 28 92.3 26 91.9 39 89.4 57 89.5 57 90.5 36 91.9 32 91.7 32 a. Find the equation of the least squares line for the data. b. Use the equation in part a to find the expected number of calories in a soup that is 87% water. c. Determine the correlation coefficient of the data.The article “Characterization of Highway Runoff in Austin, Texas, Area” (J. of Envir. Engr., 1998: 131–137) gave a scatterplot, along with the least squares line, of x = rainfall volume (m3) and y = runoff volume (m3) for a particular location. The accompanying values were read from the plot. x <‐ c(5, 12, 14, 17, 23, 30, 40, 47, 55, 67, 72, 81, 96, 112, 127) y <‐ c(4, 10, 13, 15, 15, 25, 27, 46, 38, 46, 53, 70, 82, 99, 100) Test at level 0.05 whether there is a useful linear relationship between rainfall and runoff,and then calculate a 95% confidence interval for the true average change in runoff volumeassociated with one unit (one m3) increase in rainfall volume.
- J 2 make a 2 way ANOVA table for data on MATLAB with codeA machine filling 18-gram containers of a hair dye is set so that the average fill is18.2 grams with a variance of 0.49 grams. Assume that the filling of containers bythis machine is normally distributed.(a) What percentage of the containers is not likely to meet the producer’sspecification of at least 18 grams per container?(b) What is the minimum mass of the heaviest 15% of containers?The shape of the mean-variance frontier that results from the combination of a riskless and arisky asset is…..:a. Is U-shaped, tilted 90 degrees clockwise.b. Is a straight line passing from the mean-variance points of the two assets.c. Is a hyperbola.d. Consists of two straight lines, each connecting one of the two assets to a risk-freeportfolio
- A local group of economists wants to study the effects of the pandemic on the small businesses in their city. A survey was sent out to a random sample of small businesses to anonymously report both their weekly earnings in $1000 for January 2020 (group 1) and January 2021 (group 2). Assume that the weekly earnings are normally distributed. Only 10 businesses provided enough data to compute their average weekly earnings for two months. The groups are dependent. Use α = 0.01 to decide whether there is sufficient evidence that the pandemic reduced the average weekly earnings for small businesses. January 2020 January 2021 58.2 60.5 78.3 62.5 38.2 40.9 32.7 36.2 43.8 36.2 33.7 30.9 50.5 41.4 56.3 38.3 41.1 37.9 26.4 21.7 1. What are the correct hypotheses? H0: H1: 2. Based on the hypotheses, compute the following: Round answers to at least 4 decimal places. The test statistic is = The critical value is =…A local group of economists wants to study the effects of the pandemic on the small businesses in their city. A survey was sent out to a random sample of small businesses to anonymously report both their weekly earnings in $1000 for January 2020 (group 1) and January 2021 (group 2). Assume that the weekly earnings are normally distributed. Only 10 businesses provided enough data to compute their average weekly earnings for two months. The groups are dependent. Use α = 0.01 to decide whether there is sufficient evidence that the pandemic reduced the average weekly earnings for small businesses. January 2020 January 2021 58.5 29.7 37.1 50.8 48.4 36.8 44.8 33.9 72.9 36.5 27.9 45.6 78.5 58.4 53.4 51.2 83.4 47 48.2 33.6 1) What are the correct hypotheses? H0: H1: 2) Based on the hypotheses, compute the following: Round answers to at least 4 decimal places. The test statistic is = The critical value is =…Design a 3rd order Least-squares function approximation to interpolate between the mid between (2n and 3") for a dataset as chosen by you. Compute the LS model error.
- Calculate Pearson’s coefficient of skewness. Hence, describe the shape of thedistribution of the waiting time for counter A and B.The salaries of physicians in a certain speciality are approximately normally distributed. 25% of these physicians earn less than $180,000 and 25% earn more than $320,000. Let X be the salary (per thousand) of a randomly chosen physician in this specialty, find the mean and variance of X.Is a baseball players' slugging percentage correlated to their strikeout percentage? A random sample of n=6n=6professional baseball players gave the following data (Source: baseball-reference.com) Slugging 0.396 0.42 0.323 0.078 0.473 0.467 Strikeouts 27 14.3 30.8 47.1 17.8 36.7 Find the least squares line if we consider slugging percengtage as the explanatory variable and strikeout percentage as the response variable. (Round the y-intercept and slope to 2 decimal places.)y^ = For a unit increase in slugging percentage, how much of a decrease Correct in strikeout percentage is predicted? (Round your answer to 2 decimal places.) What percentage of the variation in strikeout percentage (yy) can be explained by slugging percentage (xx) and the least squares line? (Round to the nearest percent.) p-value (Round to four decimal places)
