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- Tom has been gathering data concerning the cost of a spa treatment, y', during the before Valentine's Day. The only independent variable that he has considered is the number of minutes, "x," in the treatment. Suppose Tom collects data on the relationship between the number of minutes in a treatment and the resulting cost of we the treatment. Tom finds that the correlation between cost and number of minutes is strong and positive. Therefore, he has performed a linear regression analysis on his data. His results are that the constant "a" is 35, and the coefficient "b1" for the independent variable is 1.3. Which of the following is the correct linear regression equation that would allow Tom to predict the cost of a spa treatment given the number of minutes? Oy = 78x + 35 Oy' = 1.3x + 35 %3D Oy = 78x - 1.3 %3D OY = -1.3x - 35The flow rate in a device used for air quality measurement depends on the pressure drop x (inches of water) across the device's filter. Suppose that for x values between 5 and 20, these two variables are related according to the simple linear regression model with true regression line y = -0.11 + 0.097x. (a.1) What is the true average flow rate for a pressure drop of 10 in.?(a.2) A drop of 15 in.?(b) What is the true average change in flow rate associated with a 1 inch increase in pressure drop?(c) What is the average change in flow rate when pressure drop decreases by 5 in.?A trucking company considered a multiple regression model for relating the dependent variable y = total daily travel time for one of its drivers (hours) to the predictors x₁ = distance traveled (miles) and x₂ = the number of deliveries made. Suppose that the model equation is Y = -0.800+ 0.060x₁ +0.900x₂ + e (a) What is the mean value of travel time when distance traveled is 50 miles and four deliveries are made? hr (b) How would you interpret ₁ = 0.060, the coefficient of the predictor x₁? O When the number of deliveries is constant, the average change in travel time associated with a ten-mile (i.e. one unit) increase in distance traveled is 0.060 hours. O The total daily travel time increases by 0.060 hours when the distance traveled increases by 1. O When the number of deliveries is held fixed, the average change in travel time associated with a one-mile (i.e. one unit) increase in distance traveled is 0.060 hours. O The average change in travel time associated with a one-mile (i.e.…
- The owner of a movie theater company used multiple regression analysis to predict gross revenue (y) as a function of television advertising (x,) and newspaper advertising (x,). The estimated regression equation was ý = 82.3 + 2.29x, + 1.90x2. The computer solution, based on a sample of eight weeks, provided SST = 25.1 and SSR = 23.415. (a) Compute and interpret R? and R 2. (Round your answers to three decimal places.) The proportion of the variability in the dependent variable that can be explained by the estimated multiple regression equation is 653 x . Adjusting for the number of independent variables in the model, the proportion of the variability in the dependent variable that can be explained by the estimated multiple regression equation is (b) When television advertising was the only independent variable, R2 = 0.653 and R,2 = 0.595. Do you prefer the multiple regression results? Explain. Multiple regression analysis (is preferred since both R2 and R.2 show an increased v v…The owner of a movie theater company used multiple regression analysis to predict gross revenue (y) as a function of television advertising (x,) and newspaper advertising (x,). The estimated regression equation was ŷ = 82.1 + 2.23x, + 1.70x2. The computer solution, based on a sample of eight weeks, provided SST = 25.1 and SSR = 23.345. (a) Compute and interpret R2 and R_2. (Round your answers to three decimal places.) . Adjusting for the number of independent variables in the model, the The proportion of the variability in the dependent variable that can be explained by the estimated multiple regression equation is proportion of the variability in the dependent variable that can be explained by the estimated multiple regression equation isLet x be the size of a house (in square feet) and y be the amount of natural gas used (therms) during a specified period. Suppose that for a particular community, x and y are related according to the simple linear regression model with the following values. ? = slope of population regression line = 0.016 ? = y intercept of population regression line = −7 Question: Graph the population regression line by first finding the point on the line corresponding to x = 1,000 and then the point corresponding to x = 2,000, and drawing a line through these points.
- The distance between the Y value in the data and the predicted Y value from the regression equation is known as the residual. What is the value for the sum of the squared residuals? a. SSresidual = r2(SSX) b. SSresidual = r2(SSY) c. SSresidual = (1 – r2)(SSX) d. SSresidual = (1 – r2)(SSY)A regression was run to determine if there is a relationship between hours of TV watched per day (xx) and number of situps a person can do (yy). The results of the regression were: y=ax+ba=-1.392b=32.952r2=0.527076r=-0.726Use this to predict the number of situps a person who watches 2 hour(s) of TV can do, and please round your answer to a whole number.An investigation into the relationship between an adolescent mother's age x in years and the birth weight y of her baby in grams yielded the regression equation y= - 1163.45 + 245.15x as well as r = .88369, r2= .78091, SSE = 337212.45, and s= 205.30844 1) What is the predicted birth weight for a baby brn to a 17 year old woman? 2) What is the propotion of the variability in the weights of babies born to adolescent mothers that is accounted for by the mother's age? 3) For every additional year in the mother's age that mean birth weight of the baby? (a) increases by about 245g (b) decreases by about 245g (c) increases by about 1163g (d) increases by about 1163g (e) changes by an amount that cannot be determined from the information given.
- The table below shows the amounts of crude oil (in thousands of barrels per day) produced by a country and the amounts of crude oil (in thousands of barrels per day) imported by a country, for the last seven years. Construct and interpret a 98% prediction interval for the amount of crude oil imported by the this country when the amount of crude oil produced by the country is 5,464 thousand barrels per day. The equation of the regression line is y=-1.106x+15,759.462 Oil_produced,_x Oil_imported,_y5,816 9,3455,741 9,1245,660 9,6325,405 10,0095,155 10,1685,059 10,1055,015 10,055B b. What does the scatter diagram developed in part (a) indicate about the relationship between the two variables? The scatter diagram indicates a positive linear relationship between a = average number of passing yar and y = the percentage of games won by the team. c. Develop the estimated regression equation that could be used to predict the percentage of games won given the avera passing yards per attempt. Enter negative value as negative number. WinPct =| |)(Yds/Att) (to 4 decimals) d. Provide an interpretation for the slope of the estimated regression equation (to 1 decimal). The slope of the estimated regression line is approximately So, for every increase : of one yar number of passes per attempt, the percentage of games won by the team increases by %. e. For the 2011 season, the average number of passing yards per attempt for the Kansas City Chiefs was was 5.5. Use th regression equation developed in part (c) to predict the percentage of games won by the Kansas City Chiefs.…The quality of the orange juice produced by a certain manufacturer is constantly monitored. Data collected on the sweetness index of an orange juice sample and amount of water-soluble pectin for 24 production runs at a juice manufacturing plant are shown in the accompanying table. Suppose a manufacturer wants to use simple linear regression to predict the sweetness (y) from the amount of pectin (x). Find and interpret the coefficient of determination, r2, and the coefficient of correlation, r. Find and interpret the coefficient of determination, r2. Select the correct choice below and fill in the answer box within your choice. (Round to three decimal places as needed.) A. The coefficient of determination, r2, is enter your response here. Sample variations in the amount of water-soluble pectin explain 100r2% of the sample variation in the sweetness index using the least squares line. B. The coefficient of determination, r2, is enter your…