4) Use the given data to find the equation of the regression line. Round the final values to three significant digits, if necessary. 4) 6. 8 20 28 36 y 13 20 30 A) y = - 2.79 + 0.950x B) y = - 3.79 + 0.897x C) y = - 2.79 + 0.897x D) y = - 3.79 + 0.801x
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Unitary Method
The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.
Speed, Time, and Distance
Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.
Profit and Loss
The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.
Units and Measurements
Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.
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- 4.For a sample of 12 observations, a businessman wants to regress the price (in dollar) of the laptop (Y) on the processor's speed (X). The summary results of the observations are given below. Σx = 19.8 , Σy = 24798, Σxy = 431882 Σx^2 = 33.88, Σγ^2 = 57365692 (b)Find the fitted regression line of the price of laptop on processor speed. (c) Find the predicted price of the laptop (y) for the processor speed x-1.9. (d) Compute the coefficient of determination and comment.Sarah is the office manager for a group of financial advisors who provide financial services for individual clients. She would like to investigate whether a relationship exists between the number of presentations made to prospective clients in a month and the number of new clients per month. The following table shows the number of presentations and corresponding new clients for a random sample of six employees. Employee Presentations New Clients 1 7 2 2 9 3 3 9 4 4 10 3 5 11 5 6 12 3 Sarah would like to use simple regression analysis to estimate the number of new clients per month based on the number of presentations made by the employee per month. The expected number of new clients per month for an employee who made 10 presentations per month is ________. 2.3982 1.6753 3.0521 3.4348Given below are seven observations collected in a regression study on two variables, x (independent variable) and y (dependent variable). Copy and paste the numbers in an Excel worksheet and then use Excel's Regression tool to conduct a simple linear regression analysis. Choose 95% confidence level. Answer the following questions: x y 2 12 3 9 6 8 7 7 8 6 7 5 9 2 Find out regression coefficient b1 (Keep 2 decimal places) Find out SSR (Keep 2 decimal places) Find out SST (Only report the integer part)
- Bill is the office manager for a group of financial advisors who provide financial services for individual clients. She would like to investigate whether a relationship exists between the number of presentations made to prospective clients in a month and the number of new clients per month. The following table shows the number of presentations and corresponding new clients for a random sample of six employees. Employee Presentations New Clients 1 2 1 2 8 2 3 9 4 4 10 3 5 11 5 6 12 6 Bill would like to use simple regression analysis to estimate the number of new clients per month based on the number of presentations made by the employee per month. The average number of new clients per month for an employee who made 20 presentations per month is ________. 5.02 5.45 3.43 8.69Given below are seven observations collected in a regression study on two variables, x (independent variable) and y (dependent variable). Copy and paste the numbers in an Excel worksheet and then use Excel's Regression tool to conduct a simple linear regression analysis. Choose 95% confidence level. Answer the following questions: x y 2 12 3 9 6 8 7 7 8 6 7 5 9 2 Find out F Statistics (Only report the integer part) F Statistics is statistically significant at 5% level. Answer Yes or No. Yes No Find out t statistics for the independent variable x (Keep 2 decimal places) t statistics is statistically significant at 5% level. Answer Yes or No. Yes No What is the lower bound of the 95% confidence interval for the independent variable x (Keep 2 decimal places) What is the upper bound of the 95% confidence interval for the independent variable x (Keep 2 decimal places)Among a group of high school students, GPA and hours spent on video games are related. The average GPA is 3.0 with SD=0.4.The average hours spent on video games are 6 hours with SD=3.r = -0.2. If a student has a GPA of 3.9, what would we predict for hours spent on video games, using the regression line to make the prediction? Choose the answer that is closest. Group of answer choices 4.5 4 5 5.5
- The heights above sea level and average winter temperatures of cities in a particular country are collected. The summary statistics for this data are as follows: Sea level: AVG = 5400 ft, SD = 2100 ftAverage winter temperatures: AVG = 40 degrees F, SD = 25 degrees Fr = -0.7 If a city is 5000 ft above sea level, what is its predicted average winter temperature, using the regression line to make the prediction? Choose the answer that is closest. Group of answer choices 50 degrees F 45 degrees F 35 degrees F 40 degrees FA random sample of 11 students produced the following data, where x is the hours spent per month playing video games, and y is the first-semester grade (out of a maximum of 80 points). The data are presented below in the table of values. x y 12 80 16 41 20 67 21 51 23 49 24 57 26 70 30 78 30 54 32 39 33 42 What is the equation of the regression line? Select the correct answer below: yˆ=−0.677x+24.3 yˆ=14.673x+24.3 yˆ=14.673x+73.5 yˆ=−0.677x+73.5For a sample of over 160 college students, the following variables were measured: Y = height X1 = mother’s height X2 = father’s height X3 = 1 if male, 0 if female The goal is to predict student’s height using the mother’s and father’s heights, and sex, where sex is categorized using the variable “male” = 1 if male, 0 if female. Question 1 The regression model is __________________________________________ Regress command results (remember that we now have n = 165 cases; we removed one outlier): Source | SS df MS Number of obs = 165 -------------+------------------------------ F( 3, 161) = 104.38 Model | 1679.17741 3 559.725803 Prob > F = 0.0000 Residual | 863.31653 161 5.36221447 R-squared = 0.6604 -------------+------------------------------ Adj R-squared = 0.6541 Total | 2542.49394 164 15.5030118 Root MSE = 2.3156…
- Suppose you are a dolphin trainer at SeaWorld. You teach the dolphins by rewarding them with fish treats after each successful attempt at a new trick. The following table lists the dolphins, the number of treats per success given to each, and the average number of attempts necessary for each to learn to perform the tricks. Dolphin Number of Treats Number of Attempts Diana 2 5 Frederick 4 4 Fatima 1 7 Marlin 3 4 You can use the preceding sample data to obtain the regression line, where Ŷ is the predicted value of Y: ŶŶ = = bX + abX + a One formula for the slope of the regression line is as follows: bb = = SPSSxSPSSx To calculate the slope, first calculate SP and SSxx: SP = , and SSxx = . (Hint: For SP use the computational formula and for SSxx use the definitional formula.) The slope of the regression line is , and the Y intercept of the regression line is . The difference between Y and Ŷ for a…A manufacturing company that produces laminate for countertops is interested in studying the relationship between the number of hours of training that an employee receives and the number of defects per countertop produced. Ten employees are randomly selected. The number of hours of training each employee has received is recorded and the number of defects on the most recent countertop produced is determined. The results are as follows. Hours of Training Defects per Countertop1 54 17 03 32 52 45 15 21 86 2 The estimated regression equation and the standard error are given. Defects per Countertop=6.717822−1.004950(Hours of Training)Se=1.229787 Suppose a new employee has had 1 hour of training. What would be the 90% prediction interval for the number of defects per countertop? Round your answer to two decimal places.A manufacturing company that produces laminate for countertops is interested in studying the relationship between the number of hours of training that an employee receives and the number of defects per countertop produced. Ten employees are randomly selected. The number of hours of training each employee has received is recorded and the number of defects on the most recent countertop produced is determined. The results are as follows. Hours of Training Defects per Countertop1 54 17 03 32 52 45 15 21 86 2 The estimated regression equation and the standard error are given. Defects per Countertop=6.717822−1.004950(Hours of Training)Se=1.229787S Suppose a new employee has had 3 hours of training. What would be the 95 prediction interval for the number of defects per countertop? Round your answer to two decimal places.