An SRS of apartment listings in a large northeastern city comparing monthly rent ($) versus size (ft²) yields the following computer output: (a) Is a linear model appropriate for these data? Explain. Rent 1,800 1,500- 1,200 900 600.. 1,000 1,250 1,500 1,750 2,000 Size Variable Coef Constant Size s = 102.4 -311.341 1.07707 R-squ = 94.7% Residuals (b) Interpret the slope of the regression line. (c) Interpret ² in context. 150 75 0- s.e. Coef 117.6 0.09047 -75- 900 1,200 1,500 2,000 Predicted Rent t Р -2.65 0.0294 11.9 0.0001 R-squ (adj) = 94.08
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An SRS of apartment listings in a large northeastern city comparing monthly rent ($) versus size (〖ft〗^2) yields following computer output:
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- In order to determine the relationship between the number of units sold of a company's product (y) in 11 cities with their major competitor's price (x1) in dollars, and the number of stores (x2) the competitor has in each city, the following data were collected. Units sold CompetitorPrice CompetitorStores 510 35 5 680 45 0 590 40 2 650 45 1 600 40 2 600 41 1 540 40 5 575 46 6 600 41 2 550 35 3 560 39 3 Generate a linear multiple regression output for the data.a) Report the regression coefficients accurate to 3 decimal places: ˆy^= ---- +------ x1 + -------x2 b) Report the coefficient of determination accurate to 3 decimal places: R2=An online market evaluation company e-Serve collects data and provides analytic solutions for sales promotion. A subsample of e-Serve for promotion expenditure and sales of several ecommerce businesses in million taka are provided below.Promotion 22 15 4 4 7 10 12 15 17 15Sales 150 100 80 100 90 120 110 120 130 140(a) Show that a simple linear regression model can be fitted with these variables and state a linear model for these variables. How the least square method is used to estimate parameters in a linear regression model?(b) At 5% level of significance test the hypothesis that the correlation is not positive. Based on the test result comment on the sign of the regression coefficient.(c) Find the regression line of sales on promotion expenditure by estimating parameters. Also, test the significance of slope coefficient at 5% level.(d) Find the 95% confidence interval for the mean sales with promotion expenditure of 7 million taka and comment on your results.Cafe michigans manager, gary starkm suspects that demand for mocha latte coffees depends on the price being charged. Based on historical observations, Gary has gathered the following data, which show the number of thesse coffees sold over six different price values: Price number sold $2.70 760 $3.50 510 $2.00 980 $4.20 250 $3.10 320 $4.05 480 Using simple linear regression and given that the price per cup is $2.80 the forecasted demand for mocha latte coffees will be [__] cups (enter your response rounded to one decimal place)
- In order to determine the relationship between the number of units sold of a company's product (yy) in 9 cities with their major competitor's price (x1x1) in dollars, and the number of stores (x2x2) the competitor has in each city, the following data were collected. Units sold CompetitorPrice CompetitorStores 510 35 5 600 44 3 600 41 2 600 40 2 650 45 1 590 40 2 600 41 1 540 40 5 590 40 2 Generate a linear multiple regression output for the data.a) Report the regression coefficients accurate to 3 decimal places:ˆyy^= + x1 + x2b) Report the coefficient of determination accurate to 3 decimal places:R2=In order to determine the relationship between the number of units sold of a company's product (yy) in 8 cities with their major competitor's price (x1x1) in dollars, and the number of stores (x2x2) the competitor has in each city, the following data were collected. Units sold CompetitorPrice CompetitorStores 545 35 3 550 35 3 590 40 2 570 39 4 540 40 5 600 40 2 575 46 6 560 39 3 Generate a linear multiple regression output for the data.The attached cost-output data were obtained as part of a study of the economies of scale in operating a charter high school in Wisconsin:What type of cost-output relationship (linear, quadratic, cubic) is suggested by these statistical results?
- The following are data on the average weekly profits(in $1,000) of five restaurants, their seating capacities, andthe average daily traffic (in thousands of cars) that passestheir locations: Seating Traffic Weekly netcapacity count profitx1 x2 y120 19 23.8200 8 24.2150 12 22.0180 15 26.2240 16 33.5 (a) Assuming that the regression is linear, estimate β0, β1,and β2.(b) Use the results of part (a) to predict the averageweekly net profit of a restaurant with a seating capacityof 210 at a location where the daily traffic count averages14,000 cars.According to "Reproductive Biology of the Aquatic Salamander Amphiuma tridactylum in Louisiana,"† the size of a female salamander's snout is correlated with the number of eggs in her clutch. The following data are consistent with summary quantities reported in the article. Partial Minitab output is also included. Snout-Vent Length Clutch Size 32 45 53 215 53 160 53 170 54 190 57 200 57 270 58 175 58 245 59 215 63 170 63 240 64 245 67 280 The regression equation is Y = -133 + 5.92x Predictor Coef Stdev T P Constant -133.02 64.30 2.07 0.0608 x 5.919 1.127 5.25 0.0002 s = 33.90 R-sq = 69.7% R-sq(adj) = 67.2% Additional summary statistics are given below. n = 14 x = 56.5 y = 201.4 Σx2 = 45,597 Σy2 = 613,550 Σxy = 164,690 You can use the Distribution Calculators page in SALT to find critical values and/or p-values to answer parts of this question. (a) What is the equation of the regression line…An article gave a scatter plot along with the least squares line of x = rainfall volume (m3) and y = runoff volume (m3) for a particular location. The accompanying values were read from the plot. x 6 12 14 16 23 30 40 47 55 67 72 83 96 112 127 y 4 10 13 15 15 25 27 45 38 46 53 67 82 99 104 (a) Does a scatter plot of the data support the use of the simple linear regression model? Yes, the scatterplot shows a reasonable linear relationship.Yes, the scatterplot shows a random scattering with no pattern. No, the scatterplot shows a reasonable linear relationship.No, the scatterplot shows a random scattering with no pattern. (b) Calculate point estimates of the slope and intercept of the population regression line. (Round your answers to four decimal places.) slope intercept (c) Calculate a point estimate of the true average runoff volume when rainfall volume is 52. (Round your answer to four decimal places.) m3(d) Calculate a point estimate of the…
- The following table shows data for the cost of natural gas in Maryland (in dollars per Million Btu) for x years since 1990. Year x Price in $ per Million Btu 1990 6.31 1991 6.14 1992 6.32 1993 6.75 1994 6.8 1995 6.34 1996 7.46 1997 8.12 1998 8.04 1999 8.25 2000 9.58 2001 11.28 2002 9.25 a. Define the explanatory and response variables for this problem. b. Use the calculator to obtain the linear regression line of best fit for the original prices; round to three decimal places. Write this prediction equation in the form: a. In a brief sentence, interpret the slope in the context of the problem.Café Michigan's manager, Gary Stark, suspects that demand for mocha latte coffees depends on the price being charged. Based on historical observations, Gary has gathered the following data, which show the numbers of these coffees sold over six different price values: Price Number Sold $2.60 760 $3.50 515 $2.10 980 $4.30 250 $3.00 315 $4.05 480 Part 2 Using simple linear regression LOADING... and given that the price per cup is $1.85, the forecasted demand for mocha latte coffees will be enter your response here cups (enter your response rounded to one decimal place).A researcher notes that, in a certain region, a disproportionate number of software millionaires were born around the year 1955. Is this a coincidence, or does birth year matter when gauging whether a software founder will besuccessful? The researcher investigated this question by analyzing the data shown in the accompanying table. Complete parts a through c below. a. Find the coefficient of determination for the simple linear regression model relating number (y) of software millionaire birthdays in a decade to total number (x) of births in the region. Interpret the result. The coefficient of determination is 1.___? (Round to three decimal places as needed.) This value indicates that 2.____ of the sample variation in the number of software millionaire birthdays is explained by the linear relationship with the total number of births in the region. (Round to one decimal place as needed.) b. Find the coefficient of determination for the simple linear regression model…