The decay of radioactive species can be expressed with the following model: а sin(Q / d) = where: t: is the time (min), and Q is the material radioactivity strength. a and b: model parameters. c: is time dependent lead which has a value of 10 d: is a strength parameter with a value of 100. Use a linear least square regression to fit the given model for the following deacy data and test the statistical goodness of the fit: t 2 8 12 14 17 20 Windows bi6.4 5.9 4.1 3.7 3.5 3.2 3

The table below shows the number of state-registered automatic weapons and the murder rate for several Northwestern states. xx 11.7 8.1 6.7 3.3 2.7 2.3 2.2 0.3 yy 13.8 10.7 9.9 6.6 6.1 5.9 6.1 4.5 xx = thousands of automatic weaponsyy = murders per 100,000 residents Determine the regression equation in y = ax + b form and write it below. (Round to 2 decimal places)   A) How many murders per 100,000 residents can be expected in a state with 6.4 thousand automatic weapons?     Answer = Round to 3 decimal places. B) How many murders per 100,000 residents can be expected in a state with 6.7 thousand automatic weapons?    Answer = Round to 3 decimal places.

Consider the accompanying data on x = research and development expenditure (millions of dollars) and y = growth rate (% per year) for eight different industries. X 2.025 5.039 0.904 3.573 1.157 0.327 0.378 0.191 y 1.90 3.96 USE SALT 2.44 0.88 0.37 -0.9 0.49 1.01 (a) Would a simple linear regression model provide useful information for predicting growth rate from research and development expenditure? Test the appropriate hypotheses using a 0.05 significance level. Calculate the test statistic. (Round your answer to two decimal places.) t = Use technology to find the P-value for this test. (Round your answer to four decimal places.) P-value = What can you conclude? O Reject Ho. We do not have convincing evidence of a useful linear relationship between growth rate and research and development expenditure. O Fail to reject Ho. We do not have convincing evidence of a useful linear relationship between growth rate and research and development expenditure. O Fail to reject H. We have…

A residual plot from a simple linear regression analysis is shown to the right. Use the plot to answer the question below. residuals 0 X Which of the following statements regarding the plot is true? OA. The condition that the residuals are normally distributed is not met since not all of the residuals fall on the reference line in the residual plot. OB. The condition that the residuals have constant variation is met since the lines connecting the largest positive residuals and largest negative residuals are parallel. Oc. The condition that the residuals are normally distributed is not met since there is a diamond shape to the residuals in the residual plot. OD. The condition that the residuals have constant variation is not met since the variation increases and then decreases as x gets larger.

The regression model Yi=−303.8+1.5949X1i−0.0699X2i predicts standby hours based on total staff​ present, X1i​, and remote​ hours, X2i​, for week i. The data from which the model was constructed are provided. b. If​ appropriate, perform the​ Durbin-Watson test, using α=0.05.   Determine the​ Durbin-Watson statistic.

Keeping water supplies clean requires regular measurement of levels of pollutants. The measurements are indirect- a typical analysis involves forming a dye by a chemical reaction with the dissolved pollutant, then passing light through the solution and measuring its " absorbence." To calibrate such measurements, the laboratory measures known standard solutions and uses regression to relate absorbence and pollutant concentration. This is usually done every day. Here is one series of data on the absorbence for different levels of nitrates. Nitrates are measured in milligrams per liter of water.   Nitrates   100 50 125 250 300 300 800 1400 1700 3800 Absorbance   5.8 7.3 13.9 20.9 49.6 92.6 142.8 185.5 203.6 236.1 Chemical theory says that these data should lie on a straight line. If the correlation is not at least 0.997, something went wrong and the calibration procedure is repeated. (a) Find the correlation r.     r =   (b) Must the calibration be done again? (Answer YES or…

A survey is conducted on 700 Californians older than 30 years of age. The study wants to obtain inference on the relationship between years of education and yearly income in dollars. The response variable is income in dollars and the explanatory variable is years of education. A simple linear regression model is fit, and the output from R is below: Im(formula = Income ~ Education, data = CA) Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 25200.25 1488.94 16.93 3.08e-10 *** Education 2905.35 112.61 25.80 1.49e-12 *** Residual standard error: 32400 on 698 degrees of freedom Multiple R-squared: 0.7602