Compute the least-squares regression line for the given data set. 4 6. 7. 8.5 8.4 10 11.3 11.9 13.1 Oy = 5.0648x + 0.9943 Oy = 0.9400x + 8.5 %D Oy = 0.9943x + 5.0648 Oy= 0.9400x + 5.0648
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- 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%…Find the required linear model using least-squares regression. The following table shows the number of operating federal credit unions in a certain country for several years. 2011 2012 2013 2014 4426 4255 4094 3919 Year Number of federal credit unions (a) The linear model for these data is y = (Round to the nearest tenth as needed.) (a) Find a linear model for these data with x = 11 corresponding to the year 2011. (b) Assuming the trend continues, estimate the number of federal credit unions in the year 2018. X + 2015 (b) The estimated number of credit unions for the year 2018 is (Round to the nearest integer as needed.) 3752Derive the least squares estimators (LSEs) of the parameters in the simple linear regression model.
- Find the required linear model using least-squares regression. The following table shows the number of operating federal credit unions in a certain country for several years. 2011 2012 2013 2014 4497 4323 4156 3976 Year Number of federal credit unions (a) The linear model for these data is y = (Round to the nearest tenth as needed.) (a) Find a linear model for these data with x = 11 corresponding to the year 2011. (b) Assuming the trend continues, estimate the number of federal credit unions in the year 2018. X + 2015 (b) The estimated number of credit unions for the year 2018 is (Round to the nearest integer as needed.) 3807The y-interept bo of a least-squares regression line has a useful interpretation only if the x-values are either all positive or all negative. Determine if the statement is true or false. Why? If the statement is false, rewrite as a true statement.A financial analyst is examining the relationship between stock prices and earnings per share. She chooses fifteen publicly traded companies at random and records for 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 = -0.137 +0.043x. This line, along with a scatter plot of her data, is shown below. Earnings per share, x (in dollars) Current stock price, y (in dollars) 59.10 2.35 30.89 1.34 40.95 1.76 29.50 1.02 48.19 1.63 37.29 1.68 21.65 0.63 15.95 0.63 1- 26.45 1.02 0.5 32.26 1.53 17.72 0.78 42.86 1.50 Earnings per share (in dollars) 36.45 1.17 57.56 2.84 40.32 1.06 Current stock price (in dollars)
- A financial analyst is examining the relationship between stock prices and earnings per share. She chooses sixteen publicly traded companies at random and records for 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 ŷ=-0.231+0.045x. This line, along with a scatter plot of her data, is shown below. Earnings per share, x Current stock price, y (in dollars) (in dollars) 58.47 2.17 30.64 1.44 41.03 1.45 41.26 1.05 26.04 0.80 42.80 1.84 18.10 0.77 21.73 0.62 29.68 0.74 32.97 1.64 37.74 1.56 57.98 2.70 38.05 1.16 49.40 1.59 15.49 0.59 51.67 2.65 Send data to calculator ✓ Send data to Excel Current stock price (in dollars) Based on the analyst's data and regression line, complete the following. 05 0 10 30 x x x **…A manager at the Camden Walmart is interested in learning more about the relationship between the number of customers in a checkout line and the total time it takes to check out. She selects a random sample of 11 customers and measured the number of customers who were in front of the selected customer in line and the time until that customer had finished checking out. An analysis of the data is provided below. Identify and interpret the y-intercept of the least squares regression line in context. Identify the coefficient of determination, r2. Interpret it in context. One of the data points appears to be an outlier. Describe this point and explain why it is considered an outlier.In a study of 1991 model cars, a researcher computed the least-squares regression line of price (in dollars) on horsepower. He obtained the following equation for this line. Price = – 6677 + 175× Horsepower Based on the least-squares regression line, what would we predict the cost to be of a 1991 model car with horsepower equal to 200? If the actual cost of a 1991 car with 200 horsepower is $27500, what is the residual? Is the predictionan underestimate or an overestimate? What does the slope of 175 and y intercept of (0,-6677) mean in the context of the problem? The coefficient of determination is ?2=84%. Interpret in the context of the problem. Find the correlation and interpret.
- Suppose John is a high school statistics teacher who believes that watching many hours of TV leads to lower test scores. Immediately after giving the most recent test, he surveyed each of the 24 students in his class and asked them how many hours of TV they watched that week. He then matched each student's test grade with his or her survey response. After compiling the data, he used hours of TV watched to predict each student's test score. He found the least-squares regression line to be ?̂ =−1.5?+85y^=−1.5x+85. He also calculated that the value of ?r, the correlation coefficient, was −0.61. Which of the choices identifies the correct value of the coefficient of determination, ?2R2, and gives a correct interpretation of its meaning?An engineer is testing a new car model to determine how its fuel efficiency, measured in L/(100 km), is related to its speed, which is measured in km/hour. The engineer calculates the average speed for 30 trials. The average speed is an example of a (statistic or parameter) The engineer would like to find the least squares regression line predicting fuel used (y) from speed (x) for the 30 cars he observed. He collected the data below. Speed 62 65 80 82 85 87 90 96 98 100 Fuel 12 13 14 13 14 14 15 15 16 15 Speed 100 102 104 107 112 114 114 117 121 122 Fuel 16 17 16 17 18 17 18 17 18 19 Speed 124 127 127 130 132 137 138 142 144 150 Fuel 18 19 20 19 21 23 22 23 24 26 The regression line equation is Round each number to four decimal places.A financial analyst is examining the relationship between stock prices and earnings per share. She chooses sixteen publicly traded companies at random and records for 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 = -0.224+0.044x. This line, along with a scatter plot of her data, is shown below. Earnings per share, x (in dollars) 30.13 42.76 58.46 37.50 57.30 27.60 30.17 41.82 50.09 38.18 22.41 33.44 39.66 14.13 17.85 53.57 Send data to calculator V Current stock price, y (in dollars) 1.41 1.37 2.25 1.54 2.64 0.90 0.79 1.04 1.56 1.15 0.65 1.72 1.80 0.51 0.71 2.74 Send data to Excel Current stock price (in dollars) Based on the analyst's data and regression line, complete the following. 2.5- 2+ 1.5. 0.5- 0…
