A study was performed on wear of a bearing y and its relationship to x1 = oil viscosity and x2 = load. The following data were obtained. y 293 230 X₁ 1.6 15.5 X₂ 851 816
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- If your graphing calculator is capable of computing a least-squares sinusoidal regression model, use it to find a second model for the data. Graph this new equation along with your first model. How do they compare?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 Predictor Variables Coefficient Std Error т P Constant -2298.36 158.531 -14.50 0.0000 Size 11598.9 230.111 50.41 0.0000 Resid. Mean Square (MSE) R-Squared Adjusted R-Squared 0.8925 1248950 0.8922 Standard Deviation 1117.56 Interpret the coefficient of determination for the regression model. A) We expect most of the sampled diamond prices to fall within $2235.12 of their least squares predicted values. B) For every 1-carat increase in the size of a diamond, we estimate that the price of the diamond will increase by $1117.56. C) There is sufficient evidence to indicate that the size of the diamond is a useful predictor of the price of a diamond when testing at alpha =…Interpret the least squares regression line of this data set. Meteorologists in a seaside town wanted to understand how their annual rainfall is affected by the temperature of coastal waters. For the past few years, they monitored the average temperature of coastal waters (in Celsius), x, as well as the annual rainfall (in millimetres), y. Rainfall statistics • The mean of the x-values is 11.503. • The mean of the y-values is 366.637. • The sample standard deviation of the x-values is 4.900. • The sample standard deviation of the y-values is 44.387. • The correlation coefficient of the data set is 0.896. The correct least squares regression line for the data set is: y = 8.116x + 273.273 Use it to complete the following sentence: The least squares regression line predicts an additional annual rainfall if the average temperature of coastal waters increases by one degree millimetres of Celsius.
- Use the least squares regression line of this data set to predict a value. Meteorologists in a seaside town wanted to understand how their annual rainfall is affected by the temperature of coastal waters. For the past few years, they monitored the average temperature of coastal waters (in Celsius), x, as well as the annual rainfall (in millimetres), y. Rainfall statistics • The mean of the x-values is 11.503. • The mean of the y-values is 366.637. • The sample standard deviation of the x-values is 4.900. • The sample standard deviation of the y-values is 44.387. • The correlation coefficient of the data set is 0.896. The least squares regression line of this data set is: y = 8.116x + 273.273 How much rainfall does this line predict in a year if the average temperature of coastal waters is 15 degrees Celsius? Round your answer to the nearest integer. millimetresInterpreting 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).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 What is the correlation between the interest rate and the yield of the stock?
- 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 Predict the price when the prime interest rate is 6%. Round the answer to at least four decimal places.Observations are taken on sales of a certain mountain bike in 30 sporting goods stores. The regression model was Y= total sales (thousands of dollars), X1 = display floor space (square meters), X2 = competitors' advertising expenditures (thousands of dollars), X3 = advertised price (dollars per unit). Coefficient 1,263.91 Predictor Intercept FloorSpace CompetingAds Price 11.29 -6.889 -0.1446 (a) Write the fitted regression equation. (Round your coefficient CompetingAds to 3 decimal places, coefficient Price to 4 decimal places, and other values to 2 decimal places. Negative values should be indicated by a minus sign.) FloorSpace - |* CompetingAds +[ * Price (b-1) The coefficient of FloorSpace says that each additional square foot of floor space O takes away 11.29 from sales (in thousands of dollars). O adds about 11.29 to sales (in thousands of dollars). O takes away 0.1496 from sales (in thousands of dollars). O adds about 6.889 to sales (in thousands of dollars). (b-2) The…The authors of the paper "Weight-Bearing Activity during Youth Is a More Important Factor for Peak Bone Mass than Calcium Intake"t used a multiple regression model to describe the relationship between y = bone mineral density (g/cm³) body weight (kg) X1 %3D X2 = a measure of weight-bearing activity, with higher values indicating greater activity (a) The authors concluded that both body weight and weight-bearing activity were important predictors of bone mineral density and that there was no significant interaction between body weight and weight-bearing activity. What multiple regression function is consistent with this description? (Use a to represent the intercept. Use B, and ß, for the coefficients of x, and x2.) y = (b) The value of the coefficient of body weight in the multiple regression function given in the paper is 0.569. Interpret this value. O When the measure of weight-bearing activity is fixed, and body weight is increased by 0.569-kg, the mean bone mineral density…
- A regression was run to determine if there is a relationship between the happiness index (y) and life expectancy in years of a given country (x).The results of the regression were: ˆy=a+bxa=0.313b=0.145 (a) Write the equation of the Least Squares Regression line of the formˆy= + x(b) Which is a possible value for the correlation coefficient, r? -0.666 -1.772 1.772 0.666 (c) If a country increases its life expectancy, the happiness index will increase decrease (d) If the life expectancy is increased by 4 years in a certain country, how much will the happiness index change? Round to two decimal places.Use the regression line to predict the happiness index of a country with a life expectancy of 65 years. Round to two decimal places.Observations are taken on sales of a certain mountain bike in 30 sporting goods stores. The regression model was Y = total sales (thousands of dollars). X₁ = display floor space (square meters), X₂= competitors' advertising expenditures (thousands of dollars), X₁ = advertised price (dollars per unit). Predictor Intercept FloorSpace CompetingAds Price Coefficient 1,243.88 13.74 -6.848 -0.1461 (a) Write the fitted regression equation. (Round your coefficient CompetingAds to 3 decimal places, coefficient Price to 4 decimal places, and other values to 2 decimal places. Negative values should be indicated by a minus sign.) *FloorSpace+ *CompetingAds+ (b-1) The coefficient of FloorSpace says that each additional square foot of floor space O takes away 13.74 from sales (in thousands of dollars) O adds about 13.74 to sales (in thousands of dollars) adds about 6.848 to sales (in thousands of dollars) takes away 01496 from sales (in thousands of dollars) (b-2) The coefficient of CompetingAds…A baseball enthusiast carried out a simple linear regression to investigate whether there is a linear relationship between the number of runs scored by a player and the number of times the player was intentionally walked. Computer output from the regression analysis is shown. Variable DF Estimate SE Intercept 1 16 2.073 Intentional Walks 1 0.50 0.037 R-sq=0.63R-sq=0.63 Let β1β1 represent the slope of the population regression line used to predict the number of runs scored from the number of intentional walks in the population of baseball players. A tt-test for a slope of a regression line was conducted for the following hypotheses. H0:β1=0Ha:β1≠0 below are the options provided thank you
