11.13 Consider the following pairs of measurements: L11013 X y 8 1 5 3 4 6 6 3 27 2 7 5 2 35 a. Construct a scatterplot for these data. b. What does the scatterplot suggest about the relationship between x and y? c. Find the least squares estimates of B and ₁. d. Plot the least squares line on your scatterplot. Does the line appear to fit the data well? Explain.
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- Suppose a doctor measures the height, x, and head circumference, y, of 11 children and obtains the data below. The correlation coefficient is 0.904 and the least squares regression line is y=0.208x+11.736. Complete parts (a) and (b) below.Consider the following data: Fit a line, y = x1 + x2t, to the data using the least squares approach.Suppose a doctor measures the height, x, and head circumference, y, of 8 children and obtains the data below. Thecorrelation coefficient is 0.944 and the least squares regression line is y = 0.199x + 11.982. Complete parts (a) and (b)below.Height, x27.5 25.5 26.25 25.25 27.5 26.25 26 27.25 27.25 27 27.25 ФHead Circumference, # 17.5 17.0 17.2 17.0 17.5 17.3 17.2 17.4 17.3 17.3 17.4(a) Compute the coefficient of determination, R?R?.% (Round to one decimal place as needed.)(b) Interpret the coefficient of determination and comment on the adequacy of the linear model.Approximately % of the variation inis explained by the least-squares regression model.According to the residual plot, the linear model appears to be (Round to one decimal place as needed.)
- Consider the following data. Do heavier cars really use more gasoline? Suppose a car is chosen at random. Let x be the weight of the car (in hundreds of pounds), and let y be the miles per gallon (mpg). The following information is based on data taken from Consumer Reports (Vol. 62, No. 4). x 27 47 32 47 23 40 34 52 y 30 22 23 13 29 17 21 14 Given the least squares line = 40.9941 − 0.5263x: (a) Make a residual plot for the least-squares model. Be sure to plot the horizontal line at y = 0. (b) Use the residual plot to comment about the appropriateness of the least squares model for these data. The residuals do not seem to be scattered randomly around the horizontal line at 0. There do not appear to be any outliers.The residuals seem to be scattered randomly around the horizontal line at 0. There do not appear to be any outliers. The residuals do not seem to be scattered randomly around the horizontal line at 0. There do appear to be outliers.The residuals…Suppose a doctor measures the height, x, and head circumference, y, of 11 children and obtains the data below. The correlation coefficient is 0.899 and the least squares regression line is y=0.185x+12.276. Complete parts (a) and (b) below. Height, x 27.75 25.75 26.75 25.75 28 26.5 25.75 26.75 27 27.25 27.25 Head Circumference, y 17.4 17.1 17.2 16.9 17.4 17.1 17.1 17.3 17.3 17.3 17.4 (a) Compute the coefficient of determination, R2. R2=nothing% (Round to one decimal place as needed.) (b) Interpret the coefficient of determination. Approximately nothing% of the variation in ▼ height head circumference is explained by the least-squares regression model. (Round to one decimal place as needed.)The 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 researchers reported:" A 2x2 ANOVA revealed, first of all, a main effect for depletion, indicating that depleted individuals generated less ideas (M = 9.40, SD = 5.64) than non-depleted individuals (M = 12.44, SD = 7.34), F (1, 108) = 6.03, p = .016, n2 = .05. This effect was qualified by the expected interaction with [perseverance], F (1,108) = 4.52, p = .036, n2 = .05". What size are the effects for the main effect of depletion and for the interaction between depletion and perseverance, according to Cohen's conventions? a. These are small- to -medium effects b. These are non existent effects c. These are large effects d. We are unable to tell from from the n2 / r2 statisticsIn the manufacture of synthetic fiber, the fiber is often “set” by subjecting it to high temperatures. The object is to improve the shrinkage properties of the fiber. In a test of 23 yarn specimens, the relationship between temperature in °C (x) and shrinkage in % (y) was summarized by the least-squares line y = −12.789 + 0.133x. The total sum of square was ∑ni=1(yi−y⎯⎯)2∑i=1n(yi−y¯)2 = 57.313, and the estimated error variance was s2 = 0.0670. Compute the coefficient of determination r 2. Round the answer to three decimal places.The following data represent the time between eruptions and the length of eruption for 9 randomly selected geyser eruptions. The coefficient of determination is 85.7%.Provide an interpretation of this value. Time, x Length, y Time, x Length, y 12.17 1.87 11.75 1.72 11.59 1.77 12.26 1.90 12.05 1.84 11.63 1.75 12.15 1.81 11.66 1.75 11.33 1.63 The least-squares regression line explains nothing ____% of the variation in_________ ▼ length of eruption. time between eruptions. (Round to one decimal place as needed.)
- A simple random sample of heights of 6400Englishmen has a mean of 67.85 inches and SD 2.56 inches, while a simple random sample of heights of 1600 Australians has a mean of 68.55 inches and SD of 2.52 inches. D the data indicate that Australians are, on the average, taller than Englishmen?The following table shows how many weeks a sample of 6 persons have worked at an automobile inspection station and on any given day: a) Find the least squares estimators and the values for a and b ??? = ___________ ? = ___________ ??? = ___________ ? = ___________ ??? = ___________ b) Determine AND WRITE the equation for the best fit line. c) Find the correlation coefficient, r, and describe the relationship between weeks in the program and time improvement.2. The following passage is from a paper. Also significant was the proportion of males and their water consumption (8 oz. servings) compared to females (X2 = 8.136, P-value = 0.087). Males came closer to meeting recommended daily water intake (64 oz. or more) than females (29.8% vs. 20.9%). This statement was based on carrying out a chi-square test of homogeneity using data in a two-way table where rows corresponded to sex (male, female) and columns corresponded to number of servings of water consumed per day, with categories none, one, two to three, four to five, and six or more. A) What hypotheses did the researchers test? H0: Sex and number of servings of water consumed per day are not independent. Ha: Sex and number of servings of water consumed per day are independent. H0: The proportions falling into each of the water categories are the same for both sexes.Ha: The proportions falling into each of the water categories are not the same for both sexes. H0: The…