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- Time to determine the temperature change along a wallcountermeasurements were taken. Using the least squares method,Describe the temperature change as a function of time with the data.t (min) 0 1 2 3 4 5 6T (o C) 20 23 33 34 56 79 98Compute the sum-of-squares error (SSE) by hand for the given set of data and linear model. (4, 4), (5, 5), (6, 7); y = x − 1 SSE=For a sample of 15 trees, the volume of lumber (y) (in cubic meters) and the diameter (x) (in centimeters) at a fixed height above ground level was measured. The following summary statistics were obtained: x̄ = 35.2 sx = 8.9 ȳ = 0.78 sy = 0.48 r = 0.95 a) Compute the least-squares regression line for predicting volume from diameter. B)Predict the volume for a tree whose diameter is 42 centimeters
- Representative data read from a plot on runoff sediment concentration for plots with varying amounts of grazing damage, measured by the percentage of bare ground in the plot, are given for steeply sloped plots. Steeply Sloped Plots Bare ground (%) 7 7 14 21 28 35 28 42 49 56 49 Concentration 80 200 240 480 400 400 720 640 880 960 800 (a) Using the data for steeply sloped plots, find the equation of the least-squares line for predicting y runoff sediment concentration using x = percentage of bare ground. (Give the answer to two decimal places.) y hat = (b) What would you predict runoff sediment concentration to be for a steeply sloped plot with 18% bare ground? (Round your answer to the nearest whole number.)For the past decade, rubber powder has been used in asphalt cement to improve performance. An article includes a regression of y = axial strength (MPa) on x = cube strength (MPa) based on the following sample data: x 112.3 97.0 92.7 86.0 102.0 99.2 95.8 103.5 89.0 86.7 y 75.4 71.3 58.1 48.5 74.1 73.7 67.7 59.5 58.0 48.6 (a) Obtain the equation of the least squares line. (Round all numerical values to four decimal places.)y = Interpret the slope. A one MPa increase in axial strength is associated with an increase in the predicted cube strength equal to the slope.A one MPa decrease in cube strength is associated with an increase in the predicted axial strength equal to the slope. A one MPa increase in cube strength is associated with an increase in the predicted axial strength equal to the slope.A one MPa decrease in axial strength is associated with an increase in the predicted cube strength equal to the slope. (b) Calculate the coefficient of determination.…For the past decade, rubber powder has been used in asphalt cement to improve performance. An article includes a regression of y = axial strength (MPa) on x = cube strength (MPa) based on the following sample data: x 112.3 97.0 92.7 86.0 102.0 99.2 95.8 103.5 89.0 86.7 y 74.6 71.1 57.5 48.4 74.0 72.9 68.3 59.8 57.6 48.0 (a) Obtain the equation of the least squares line. (Round all numerical values to four decimal places.)y = −32.6485+0.9943x Interpret the slope. A one MPa increase in axial strength is associated with an increase in the predicted cube strength equal to the slope.A one MPa decrease in cube strength is associated with an increase in the predicted axial strength equal to the slope. A one MPa decrease in axial strength is associated with an increase in the predicted cube strength equal to the slope.A one MPa increase in cube strength is associated with an increase in the predicted axial strength equal to the slope. (b) Calculate the coefficient of…
- Representative data read from a plot on runoff sediment concentration for plots with varying amounts of grazing damage, measured by the percentage of bare ground in the plot, are given for steeply sloped plots. Steeply Sloped Plots Bare ground (%) 7 7 14 21 28 35 28 42 49 56 49 Concentration 120 300 360 720 600 600 1080 960 1320 1440 1200 (a) Using the data for steeply sloped plots, find the equation of the least-squares line for predicting y runoff sediment concentration using x = percentage of bare ground. (Give the answer to two decimal places.) =________ (b) What would you predict runoff sediment concentration to be for a steeply sloped plot with 16% bare ground? (Round your answer to the nearest whole number.) _________The accompanying data were compiled by the admissions office at a college during the past 5 years. The data relate the number of college brochures and follow-up letters (x) sent to a preselected list of high school juniors who had taken the PSAT and the number of completed applications (y) received from these students (both measured in units of a thousand). x 4 4.5 5 5.5 6 y 0.5 0.7 0.9 1 1.3 (a) Determine the equation of the least-squares line for these data.y =while using the t-test to test whether regression is significant, in the model yi=β0+β1xi+εiyi=β0+β1xi+εi, what is the calculated student-t statistics (H0:β1=0H0:β1=0 versus H1:β1≠0H1:β1≠0). Calculate the least squares estimates of β0β0 in the model yi=β0+β1xi+εi Calculate the sum of squares of y denoted by Syy , the sum of squares of x denoted by Sxx and sum of squares (products) of x and y denoted by Sxy while using analysis of variance (ANOVA) to test whether regression is significant, in the model yi=β0+β1xi+εiyi=β0+β1xi+εi, what is the residual or error sum of squares due to regression, SSE. kindly help with this question
- Use the least-squares equation for the table below to predict the depth of an earthquake that measures 3.8 on the Richter scale? x = earthquake magnitude 2.9 4.2 3.3 4.5 2.6 3.2 3.4 y = depth of earthquake (in km) 5 10 11.2 10 7.9 3.9 5.5An owner of a home in the Midwest installed solar panels to reduce heating costs. After installing the solar panels, he measured the amount of natural gas used ? (in cubic feet) to heat the home and outside temperature ? (in degree‑days, where a day’s degree‑days are the number of degrees its average temperature falls below 65 ∘F ) over a 23-month period. He then computed the least‑squares regression line for predicting ? from ? and found it to be ?̂ =85+16?. By looking at the equation of the least‑squares regression line, you can see that the correlation between amount of gas used and degree‑days isRecords at a company for the last 5 years show the following relationship between the units sold (in thousands) and the price of a product. Sales Price (y) $8.80 $8.00 $7.50 $6.90 $6.20 Units Sold (x) (in thousands) 3.7 5.5 6.7 7.8 9.3 a. Find the least-squares regression line for the price in terms of thousands of units sold. Round the coefficients to three decimal places. b. Estimate the price that should be charged in order to sell 10,000 units. Round your answer to the nearest cent.