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Consumption of Coffee in the U.S. Coffee consumption in the United States is greater on a per capita basis than anywhere else in the world. However, due to price fluctuations of coffee beans and worries over the health effects of caffeine, coffee consumption has varied considerably over the years. According to data published in The Wall Street Journal, the number of cups
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Calculus & Its Applications
- Is carbon dating? Why does it work? Give an example in which carbon dating would be useful.arrow_forwardDoes a linear, exponential, or logarithmic model best fit the data in Table 2? Find the model.arrow_forwardWhat might a scatterplot of data points look like if it were best described by a logarithmic model?arrow_forward
- With what kind of exponential model would half-life be associated? What role does half-life play in these models?arrow_forwardTable 6 shows the year and the number ofpeople unemployed in a particular city for several years. Determine whether the trend appears linear. If so, and assuming the trend continues, in what year will the number of unemployed reach 5 people?arrow_forwardWorld Population The following table shows world population N, in billions, in the given year. Year 1950 1960 1970 1980 1990 2000 2010 N 2.56 3.04 3.71 4.45 5.29 6.09 6.85 a. Use regression to find a logistic model for world population. b. What r value do these data yield for humans on planet Earth? c. According to the logistic model using these data, what is the carrying capacity of planet Earth for humans? d. According to this model, when will world population reach 90 of carrying capacity? Round to the nearest year. Note: This represents a rather naive analysis of world population.arrow_forward
- Table 3 gives the annual sales (in millions of dollars) of a product from 1998 to 20006. What was the average rate of change of annual sales (a) between 2001 and 2002, and (b) between 2001 and 2004?arrow_forward1.2. In order to prepare the dataset for modelling, it became clear that RATIO repeats with similar values. The analyst decided to regard them also as categorical variables. Amend the dataset fully in order to build a regression model. Use an ascending order in the coding structure. 1.3. Show the new amended data set and formulate the regression model that must be estimated. Apply all the changes done to the dataset in Question 1.2 and give the regression function. 1.4. The estimated response function is obtained using the coding structure of Question 1.2. Ŷ = 1.34 + 0.034X₁ + 0.049 X₂ -0.041 X3 + 0.029X4 +0.011 X5 +0.08X6. Explain the regression coefficients b₁, b, and b. 1.5. Find the fitted response function for the rotational METHOD of farming on a farm with RATIO of 0.8. 1.6. Refer to Question 1.5. The analyst has a suspicion that there is interaction between the size and the age of the farm if the method of farming is rotational and the field/land ratio is 0.8. Give the response…arrow_forwardThe income of farmers depends on various factors. To predict the income of the next year, a study was undertaken and data was gathered considering as many as possible factors that might influence the yearly income. Regression methods are used to create such a prediction function, that is, we want to predict the profit for the next year. The following were determined. X₁ = SIZE - farm size recorded x 1000 hectares X₂ = AGE - how long the farm has been in operation in years X3 = RATIO - the ratio ofland size to field size recorded as 0.5, 0.75, 0.8 and 0.9 X4 = METHOD - rotational and non rotational method of planting Ŷ INCOME the income per year recorded in x R 1 000 000.00 The partial dataset is as follows INCOME Y 1.3 2.4 3.2 1.5 2.1 a. C. Sample Quantiles 18 15 1.0- 0.8- 0.6- 04- 0.2- 0.0- SIZE X₁ 25 5 8 2 1.2 1.5 Predicted Theoretical Quantiles 45 AGE X₂ 50 20 1.1. The analyst did some exploratory analysis and below are some of the residual plots he constructed. Study the plots and…arrow_forward
- The income of farmers depends on various factors. To predict the income of the next year, a study was undertaken and data was gathered considering as many as possible factors that might influence the yearly income. Regression methods are used to create such a prediction function, that is, we want to predict the profit for the next year. The following were determined. X₁ = SIZE - farm size recorded x 1000 hectares X₂ = AGE - how long the farm has been in operation in years X3 = RATIO- the ratio of land size to field size recorded as 0.5, 0.75, 0.8 and 0.9 X4 = METHOD - rotational and non rotational method of planting Ŷ = INCOME the income per year recorded in x R 1 000 000.00 The partial dataset is as follows INCOME Y 1.3 2.4 3.2 1.5 2.1 a. C. Standardized Residual Sample Quantiles 15 20 1.0- 0.8- 0.6- 04- 02- 0.0- SIZE X₁ 25 5 8 2 1.2 1.5 Predicted Theoretical Quantiles 45 AGE X₂ 2 20 100 1.1. The analyst did some exploratory analysis and below are some of the residual plots he…arrow_forwardSheila's doctor is concerned that she may suffer from gestational diabetes (high blood glucose levels during pregnancy). There is variation both in the actual glucose level and in the blood test that measures the level. A patient is classified as having gestational diabetes if the glucose level is above 140 miligrams per deciliter (mg/dl) one hour after having a sugary drink. Sheila's measured glucose level one hour after the sugary drink varies according to the Normal distribution with μμ = 120 mg/dl and σσ = 10 mg/dl. (a) If a single glucose measurement is made, what is the probability that Sheila is diagnosed as having gestational diabetes?(b) If measurements are made on 5 separate days and the mean result is compared with the criterion 140 mg/dl, what is the probability that Sheila is diagnosed as having gestational diabetes?arrow_forwardData contains brain mass in different species versus glia-neuron ratio, the latter being a measurement of brain metabolism as the glia provides the metabolic needs of the neurons. The relationship between THE LOGARITHM of the brain mass (in the third column) and Glia-neuron ratio (fourth column) appears linear and it is these two variables that we wish to analyze via linear regression. We would like to know if the human brain fits the trend from the other species. Towards this end we will perform the regression on all species EXCEPT humans (Homo sapiens). Again, throw out the human data from your analysis. You will however need the human numbers for some of the questions. What is the lower & upper bound of the 95% confidence interval for the slope of the regression line? What is the value of the t-statistic used to test the null hypothesis of zero slope via a t-test? A t-test would reject the null hypothesis at a 0.05 significance level. True Falsearrow_forward
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