Stats The dataset below presents the number of hours a small coffee shop spent promoting their newseasonal drink each week and the corresponding number of drinks sold that week.Hours on13.510.8 12.014.513.7 8.111.9 9.79.810.8Promotion (X)Drinks Sold (Y)88818393906186677069(a)Find the equation of the least squares regression line using the information below:n=10, Σx=114.8, Σx=1354.82, y = 788, Σy? =63210,Σxy=9238.9, x=11.48, y=78.8, sx =2.0253, sy=11.1335, r=0.9494(Show the details of your work.)(b)The coffee shop owner plans to spend 16 hours on promotion next week, which exceedsany recorded promotion hours. Use the regression line equation from part (a) to predict thenumber of drinks that will be sold if 16 hours are spent on promotion.(c) (4 pts) Calculate and interpret the coefficient of determination.

Answered: Image /qna-images/answer/fe7cd6e3-ab52-4122-b6ed-26ea8b9d7c3f.jpg

Answered: The dataset below presents the number…

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter5: Inner Product Spaces

Section5.CR: Review Exercises

Problem 62CR

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Find the equation of the regression line for the following data set. x 1 2 3 y 0 3 4
Olympic Pole Vault The graph in Figure 7 indicates that in recent years the winning Olympic men’s pole vault height has fallen below the value predicted by the regression line in Example 2. This might have occurred because when the pole vault was a new event there was much room for improvement in vaulters’ performances, whereas now even the best training can produce only incremental advances. Let’s see whether concentrating on more recent results gives a better predictor of future records. (a) Use the data in Table 2 (page 176) to complete the table of winning pole vault heights shown in the margin. (Note that we are using x=0 to correspond to the year 1972, where this restricted data set begins.) (b) Find the regression line for the data in part ‚(a). (c) Plot the data and the regression line on the same axes. Does the regression line seem to provide a good model for the data? (d) What does the regression line predict as the winning pole vault height for the 2012 Olympics? Compare this predicted value to the actual 2012 winning height of 5.97 m, as described on page 177. Has this new regression line provided a better prediction than the line in Example 2?
XYZ Corporation Stock Prices The following table shows the average stock price, in dollars, of XYZ Corporation in the given month. Month Stock price January 2011 43.71 February 2011 44.22 March 2011 44.44 April 2011 45.17 May 2011 45.97 a. Find the equation of the regression line. Round the regression coefficients to three decimal places. b. Plot the data points and the regression line. c. Explain in practical terms the meaning of the slope of the regression line. d. Based on the trend of the regression line, what do you predict the stock price to be in January 2012? January 2013?
Life Expectancy The following table shows the average life expectancy, in years, of a child born in the given year42 Life expectancy 2005 77.6 2007 78.1 2009 78.5 2011 78.7 2013 78.8 a. Find the equation of the regression line, and explain the meaning of its slope. b. Plot the data points and the regression line. c. Explain in practical terms the meaning of the slope of the regression line. d. Based on the trend of the regression line, what do you predict as the life expectancy of a child born in 2019? e. Based on the trend of the regression line, what do you predict as the life expectancy of a child born in 1580?2300
An engineer wants to determine how the weight of a gas-powered car, x, affects gas mileage, y. The accompanying data represent the weights of various domestic cars and their miles per gallon in the city for the most recent model year Find the least-squares regression line treating weight as the explanatory variable and miles per gallon as the response variable. y=enter your response herex+enter your response here (Round the x coefficient to five decimal places as needed. Round the constant to two decimal places as needed.)
The data in the table represent the number of licensed drivers in various age groups and the number of fatal accidents within the age group by gender. Complete parts (a) to (c) below. ..... (a) Find the least-squares regression line for males treating the number of licensed drivers as the explanatory variable, x, and the number of fatal crashes, y, as the response variable. Repeat this procedure for females. Find the least-squares regression line for males. y=x+O Data for licensed drivers by age and gender. (Round the slope to three decimal places and round the constant to the nearest integer as needed.) Find the least-squares regression line for females. x + Number of Number of Number of Male Fatal Number of Female Fatal (Round the slope to three decimal places and round the constant to the nearest integer as needed.) Licensed Drivers Crashes Licensed Drivers Crashes (b) Interpret the slope of the least-squares regression line for each gender, if appropriate. How might an insurance…
The following gives the number of accidents that occurred on Florida State Highway 101 during the last 4 months: Month Number of Accidents Jan 25 Feb 40 Mar 60 Apr 90 Using the least-squares regression method, the trend equation for forecasting is (round your responses to two decimal places): ŷ-0-0x Using least-squares regression, the forecast for the number of accidents that will occur in the month of May = accidents (enter your response as a whole number).
s is the typical amount by which the (BMI Change, Depression Score Change) value what is predicted using the least squares regression line.
What is the relationship between diamond price and carat size? 307 diamonds were sampled and a straight-line relationship was hypothesized between y = diamond price (in dollars) and x = size of the diamond (in carats). The simple linear regression for the analysis is shown below: Least Squares Linear Regression of PRICE Interpret the standard deviation of the regression model. a) We expect most of the sampled diamond prices to fall within $1117.56 of their least squares predicted values. b) We can explain 89.25% of the variation in the sampled diamond prices around their mean using the size of the diamond in a linear model. c) For every 1-carat increase in the size of a diamond, we estimate that the price of the diamond will increase by $1117.56. d) We expect most of the sampled diamond prices to fall within $2235.12 of their least squares predicted values.
The rental of an apartment (R) near campus is a function of the square footage (Sq). A random sample of apartments near campus yielded the following summary statistics: R= $350, Sq = 100, sR = $ 30, and 8 są = 10. Suppose also that the correlation between price and weight is 0.8. (a) Write the implied least squares linear regression equation. (b) Suppose an apartment has 75 sqft. Predict its price based on the above model. (c) Suppose the true rental of the apartment in part (b) is $ 325. What is the value of the residual?
Interpreting technology: The following display from the TI-84 Plus calculator presents the least-squares regression line for predicting the price of a certain stock y from the prime interest rate in percent x. LinReg y=a+bx a=2.29525776 b=0.38970413 r^2=0.4319044662 r=0.65719439 Write the equation of the least-squares regression line. Use the full accuracy shown in the calculator output (do not round your answers).
The Heights and Weights of 500 preschoolers have correlation r=0.52. The average height is 30.12 Inches, the average weight is 40.90 Pounds, the standard deviation of their heights is 4.16 inches, and the standard deviation of their weight is 6.42 Pounds. 1. What is the equation of the least squares regression line for predicting their weights from their heights? 2. I'm 35 Inches Tall- Predict my weight.

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