Chapter 12, Problem 12.55LB

Suppose Wesley is a marine biologist who is interested in the relationship between the age and the size of male Dungeness crabs. Wesley collects data on 1,000 crabs and uses the data to develop the following least-squares regression line where ?X is the age of the crab in months and ?ˆY^ is the predicted value of ?Y, the size of the male crab in cm. ?ˆ=9.1367+0.4817��Y^=9.1367+0.4817X   What is the value of ?ˆY^ when a male crab is 22.1725 months old? Provide your answer with precision to two decimal places.

Please answer as many as your allowed too. Thank you :) A regression was run to determine if there is a relationship between the happiness index (y) and life expectancy in years of a given country (x).The results of the regression were: ˆyy^=a+bxa=-1.68b=0.168 (a) Write the equation of the Least Squares Regression line of the formˆyy^= + x(b) Which is a possible value for the correlation coefficient, rr? -1.417 1.417 0.702 -0.702 (c) If a country increases its life expectancy, the happiness index will increase decrease (d) If the life expectancy is increased by 0.5 years in a certain country, how much will the happiness index change? Round to two decimal places.(e) Use the regression line to predict the happiness index of a country with a life expectancy of 69 years. Round to two decimal places.

A collection of paired data consists of the number of years that students have studied Spanish and their scores on a Spanish language proficiency test. A computer program was used to obtain the least squares linear regression line and the computer output is shown below. Along with the paired sample data, the program was also given an x value of 2 (years of study) to be used for predicting te For a person who studies for 2 years, obtain the 95% prediction interval and write a statement interpreting the interval.     (42.72, 63.98); We can be 95% confident that the test score of an individual who studies 2 years will lie in the interval (42.72, 63.98)     (31.61, 75.09); We can be 95% confident that the test score of an individual who studies 2 years will lie in the interval (31.61, 75.09)     (42.72, 63.98); We can be 95% confident that the mean test score of all individuals who study 2 years will lie in the interval (42.72, 63.98)     (31.61, 75.09); We can be 95%…

Each of 25 teenage girls with one brother was asked to provide her own height (y), in inches, and the height (x), in inches, of her brother. The scatterplot below displays the results. Only 22 of the 25 pairs are distinguishable because some of the (x,y) pairs were the same. The equation of the least-squares regression line is ŷ = 35.1 + 0.427x.*Girls are on the y-axis and brothers are on the x-axis* a.) Draw the least-squares regression line on the scatterplot above. b.)  One brother’s height was x = 67 inches and his sister’s height was y = 61 inches. Circle the point on the scatterplot above that represents this pair and draw the segment on the scatterplot that corresponds to the residual for it. Give a numerical for the residual. c.)  Suppose the point x = 84 , y = 71 is added to the data set. Would the slope of the least squares regression line increase, decrease, or remain about the same?Explain. Would the correlation increase, decrease, or remain about the same? Explain.

When a least squares line is fit to the 8 observations in the fuel consumption data, we obtain SSE = 3.264. Calculate s? and s. (Round your answers to 3 decimal places.)

A financial analyst is examinıng the Pela each the company's current stock price and the company's earnings per share reported for the past 12 months. Her data are given below, with x denoting the earnings per share from the previous year, and y denoting the current stock price (both in dollars). Based on these data, she computes the least-squares regression line to be y = -0.147+0.043x. This line, along with a scatter plot of her data, is shown below. Earnings per Current stock price, y (in dollars) share, x (in dollars) 36.55 1.64 14.18 0.57 41.79 1.37 39.16 1.10 2.5+ 57.70 2.71 26.95 0.90 32.65 1.70 41.94 1.17 52.79 2.56 42.72 2.01 16.89 0.76 22.46 0.58 Earnings per share, x (in dollars) 58.88 2.19 30.13 1.48 50.08 1.73 28.92 0.81 Submit Assi Continue D 2021 McGraw-H Education. All Rights Reserved. Terms of Use Privacy e to search 近 Current stock price, y (in dollars)

John's parents recorded his height at various ages up to 66 months. They decide to use the least- squares regression line of John's height on age to predict his height at age 21 years (252 months). We conclude: O John's height, in inches, should be about half his age, in months. O such a prediction could be misleading, because it involves extrapolation. O that the parents will get a fairly accurate estimate of his height at age 21 years because the data are clearly correlated. none of the above.

A prospective MBA student would like to examine the factors that impact starting salary upon graduation and decides to develop a model that uses program per-year tuition as a predictor of starting salary. Data were collected for 37 full-time MBA programs offered at private universities. The least squares equation was found Y = -13258.594 + 2.422X,, where X; is the program per-year tuition and Y; is the predicted mean starting salary. To perform a residual analysis for these data, the following results are obtained. of regression have been seriously violated. Residual index plot QQ Plot of Residuals Residuals Residuals 20000 20000 -20000 -20000 -40000 40000 TO 20 Index Normal Quantile Residuals vs. Program Per-Year Tuition ($) Residuals Predicted Values vs. Residuals Predicted Values 20000 140000- 120000- 100000 80000- -20000 60000 -40000 40000- 30000 50000 4000 Program Per-Year Tuition ($) 20000 60000 70000 -20000 20000 Residuals ..... a) To evaluate whether the assumption of linearity…

Explain why Y is considered the least squares estimator of the mean of Y, µy.