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Concept explainers
Freezing temperature. A linear regression model for the propylene glycol data in Table 11 is
where
(A) Draw a
(B) Use the model to estimate the freezing temperature to the nearest degree of a solution that
is 30% propylene glycol.
(C) Use the model to estimate the percentage of propylene glycol in a solution that freezes at
15°F.
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Chapter 1 Solutions
Finite Mathematics for Business, Economics, Life Sciences and Social Sciences
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- In a linear regression model, E (y) = a + Bx, ß represents: x-intercept the change in E(y) for a one-unit increase in x variable O the change in x variable for a one-unit increase in y variable. Oy-intercept Ocorrelationarrow_forwardThe table shows the average weekly wages (in dollars) for state government employees and federal government employees for 8 years. The equation of the regression line is y=1.410x−17.174. Complete parts (a) and(b) below.arrow_forwardThe least-squares regression equation is y = 602.1x + 17,023 where y is the median income and x is the percentage of 25 years and older with at least a bachelor's degree in the region. The scatter diagram indicates a linear relation between the two variables with a correlation coefficient of 0.6748. Complete parts (a) through (d). C Median Income 55000- 25000 ● (c) Interpret the slope. Select the correct choice below and fill in the answer box to complete your choice. (Type an integer or decimal. Do not round.) A. For 0% of adults having a bachelor's degree, the median income is predicted to be $ B. For a median income of $0, the percent of adults with a bachelor's degree is %. O C. For every dollar increase in median income, the percent of adults having at least a bachelor's degree is %, on average. OD. For every percent increase in adults having at least a bachelor's degree, the median income increases by $, on average. 15 20 25 30 35 40 45 50 55 60 Bachelor's % U (a) Predict the…arrow_forward
- The accompanying data was read from a graph. The independent variable is SO2 deposition rate (mg/m2/d) and the dependent variable is steel weight loss (g/m2). x 15 18 40 43 45 113 y 280 350 460 500 560 1140 (a) Construct a scatter plot. Does the simple linear regression model appear to be reasonable in this situation? Yes, the scatter plot shows a reasonable linear relationship.No, the scatter plot does not show a reasonable linear relationship. (b) Calculate the equation of the estimated regression line. (Round all numerical values to two decimal places.)y = (c) What percentage of observed variation in steel weight loss can be attributed to the model relationship in combination with variation in deposition rate? (Round your answer to one decimal place.) %(d) Because the largest x value in the sample greatly exceeds the others, this observation may have been very influential in determining the equation of the line. Delete this observation and…arrow_forwardThe data set was obtained from 21 days of operation of a plant for the oxidation of ammonia to nitric acid. It is desired to fit a multiple linear regression model to predict Y = stack loss which is 10 times the percentage of the ingoing ammonia to the plant that escapes from the absorption column unabsorbed, as Y = Bo + B1Xair.flow + B2 water.temp + B3 xacid.conc Air.Flow represents the rate of operation of the plant. Water.Temp is the temperature of cooling water circulated through coils in the absorption tower. Acid.Conc is the concentration of the acid circulating, minus 50, times 10. This is the result of the best subsets regression. |Summary of best subsets, variable(s): stack.loss (stt 151astackloss) Adjusted R square and standardized regression coefficients for each submodel Adjusted R square 0.898623 No. of Effects Air. Flow Water.Temp Acid.Conc. Subset No. 1 2 0.604950 0.402523 This is the result of the forward stepwise regression. Degr. of Freedom P to enter 0.000000 Effect…arrow_forwardA chemistry experiment is performed measuring the solubility of potassium chloride (KCl) in water at different temperatures. The goal was to determine if there is a linear relationship between the temperature of the water and how much KCl can dissolve, measured as grams per 100 milliliter (g/100mL). After the experiments were performed, the following data was collected with temperature being the independent x-variable and solubility being the dependent y-variable: Temperature (°C) x Solubility (g/100mL) y 10 31 20 33 30 37 40 41 50 42 Based on the data given for temperature and solubility of KCl and without doing any math yet, which of the following do you predict would best describe the relationship between these variables? A positive linear relationship (r close to 1) A positive linear relationship (r close to -1) A negative linear relationship (r close to 1) A negative linear relationship (r close to -1)…arrow_forward
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