In a company introducing a new product on the market it was decided to build a model explaining the dependence of the sales volume Y (in thousands of units) on the tested price of the product X_1 (in PLN) and expenditure on promotion and advertising of the product X_2 (in thousands of PLN). Based on the data given in the table below
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- The Pilot Pen Company has decided to use 15 test markets to examine the sensitivity of demand for its new product to various prices, as shown in the following table. Advertising effort was identical in each market. Each market had approximately the same level of business activity and population.a. Using a linear regression model, estimate the demand function for Pilot’s new pen.b. Evaluate this model by computing the coefficient of determination and by performing a t-test of the significance of the price variable.c. What is the price elasticity of demand at a price of 50 cents? TEST MARKET PRICE CHARGED (¢) QUANTITY SOLD(THOUSANDS OF PENS) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 50 50 55 55 60 60 65 65 70 70¢ 80 80 90¢ 90 40 20.0 21.0 19.0 19.5 20.5 19.0 16.0 15.0 14.5 15.5 13.0 14.0 11.5 11.0 17.0A fast-food chain decided to carry out an experiment to assess the influence of advertising expenditure on sales. Different relative changes in advertising expenditure, compared to the previous year, were made in eight regions of the country, and resulting changes in sales levels were observed the accompanying table shows the results. Increase in advertising expenditure (%) 0 5 15 20 25 30 35 40 Increase in sales (%) 5 10 18 25 35 50 60 65 Determine the value of ∑X, ∑X2, ∑Y, ∑Y2, ∑XY. Where X represent independent variable and Y for dependent variable. Determine and interpret the coefficient of correlation between the two variables. Determine the value of regressions coefficients and write down the simple linear regression model.…A fast-food chain decided to carry out an experiment to assess the influence of advertising expenditure on sales. Different relative changes in advertising expenditure, compared to the previous year, were made in eight regions of the country, and resulting changes in sales levels were observed the accompanying table shows the results. Increase in advertising expenditure (%) 0 5 15 20 25 30 35 40 Increase in sales (%) 5 10 18 25 35 50 60 65 Determine the value of ∑X, ∑X2, ∑Y, ∑Y2, ∑XY. Where X represent independent variable and Y for dependent variable. Determine and interpret the coefficient of correlation between the two variables. Determine the value of regressions coefficients and write down the simple linear regression model. Test the validity of the model…
- A survey of 28 employed workers found that the correlation coefficient between the number of years of post-secondary education and current annual income in dollars is -0.38. The researchers hypothesize a positive relationship between number of years of post-secondary education and annual income. What can the researchers conclude with α = 0.05? a) Obtain/compute the appropriate values to make a decision about H0. critical value= test statistic= b) effect size= C) 1)There is a significant positive relationship between years of post-secondary education and current annual income. 2)There is a significant negative relationship between years of post-secondary education and current annual income. 3) There is no significant relationship between years of post-secondary education and current annual income.Here is a dataset containing plant growth measurements of plants grown in solutions of commonly-found chemicals in roadway runoff.Phragmites australis, a fast-growing non-native grass common to roadsides and disturbed wetlands of Tidewater Virginia, was grown in a greenhouse and watered with either: Distilled water (control); A weak petroleum solution (representing standard roadway runoff); Sodium chloride solution; Magnesium chloride solution; De-icing brine (50% sodium chloride and 50% magnesium chloride).Twenty grass preparations were used for each solution, and total growth (in cm) was recorded after watering every other day for 40 days.-Perform the correct statistical test to determine the p-value.-Report your answer rounded to four decimal places.-You should use formulas, functions, and the Data Analysis ToolPak in MS Excel to avoid additive rounding errors. Here are some useful functions: =t.test(array1,array2,tails,type) Produces a p-value for any…During the spring of 1999, many fuel storage facilities in Serbia were destroyed by bombing. As a result, significant quantities of oil products were spilled and burned,resulting in soil pollution. The article “Mobility of Heavy Metals Originating from Bombing of Industrial Sites” (B. Škrbić, J. Novaković, and N. Miljević, Journal of Environmental Science and Health, 2002:7–16) reports measurements of heavy metal concentrations at several industrial sites in June 1999, just after the bombing, and again in March of 2000. At the Smederevo site, on the banks of the Danube River, eight soil specimens taken in 1999 had an average lead concentration (in mg/kg) of 10.7 with a standard deviation of 3.3. Four specimens taken in 2000 had an average lead concentration of 33.8 with a standard deviation of 0.50. Find a 95% confidence interval for the increase in lead concentration between June 1999 and March 2000.
- An urban community wants to show that the incidence of breast cancer is higher in their locality than in a neighboring rural area. (PCB levels were found to be higher in the soil of the urban community). If you find that in the urban community 20 out of 200 adult women have breast cancer and that in the rural community 10 out of 150 adult women have it, could you conclude, at a significance level of 0.05, that breast cancer is more prevalent in the urban community?1. The parameter of interest is:2. The hypotheses for this test are:3. The calculated test statistic is:4. The critical region is:5. Draw the critical region (make decision):6. It can be concluded that:Data was collected on 54 observations on a response of interest, y, and four potential predictor variables x1, x2, x3, and x4. The output from regression analyses of the data is attached to the end of the page. d) Is the variable from your best simple linear regression model (from part a) included in the model with the lowest overall MSE (part b)? Briefly explain why it could happen that the best single variable is not in the best overall model. e) Following the best subsets regression results, the sums of squares for regression and error (also called residual) are displayed for several models. Using the regression sums of squares information for the full model containing all four x variables, calculate i) the R2 value for the full model, ii) the F statistic for the test of the H0: b1 = b2 = b3 = b4 = 0, and iii) the standard deviation of the residuals for the full model. f) Using the regression sums of squares information, test the null hypothesis H0:b2 = b4 = 0 for the full model.…A deficiency of the trace element selenium in the diet can negatively impact growth, immunity, muscle and neuromuscular function, and fertility. The introduction of selenium supplements to dairy cows is justified when pastures have low selenium levels. Authors of a research paper supplied the following data on milk selenium concentration (mg/L) for a sample of cows given a selenium supplement (the treatment group) and a control sample given no supplement, both initially and after a 9-day period. Initial Measurement Treatment Control 11.2 9.1 9.6 8.7 10.1 9.7 8.5 10.8 10.3 10.9 10.6 10.6 11.7 10.1 9.7 12.3 10.8 8.8 10.3 10.4 10.4 10.9 11.2 10.4 9.4 11.6 10.6 10.9 10.7 8.4 After 9 Days Treatment Control 138.3 9.3 104 8.7 96.4 8.7 89 10.1 88 9.6 103.8 8.6 147.3 10.2 97.1 12.2 172.6 9.3 146.3 9.5 99 8.2 122.3 8.9 103 12.5 117.8 9.1 121.5 93 (a) Use the given data for the treatment group to determine if there…
- A deficiency of the trace element selenium in the diet can negatively impact growth, immunity, muscle and neuromuscular function, and fertility. The introduction of selenium supplements to dairy cows is justified when pastures have low selenium levels. Authors of a research paper supplied the following data on milk selenium concentration (mg/L) for a sample of cows given a selenium supplement (the treatment group) and a control sample given no supplement, both initially and after a 9-day period. Initial Measurement Treatment Control 11.3 9.1 9.7 8.7 10.1 9.7 8.5 10.8 10.4 10.9 10.7 10.6 11.8 10.1 9.8 12.3 10.6 8.8 10.4 10.4 10.2 10.9 11.3 10.4 9.2 11.6 10.7 10.9 10.8 8.2 After 9 Days Treatment Control 138.3 9.4 104 8.8 96.4 8.8 89 10.1 88 9.7 103.8 8.7 147.3 10.3 97.1 12.3 172.6 9.4 146.3 9.5 99 8.3 122.3 8.9 103 12.5 117.8 9.1 121.5 93 (a) Use the given data for the treatment group to determine if…A deficiency of the trace element selenium in the diet can negatively impact growth, immunity, muscle and neuromuscular function, and fertility. The introduction of selenium supplements to dairy cows is justified when pastures have low selenium levels. Authors of a research paper supplied the following data on milk selenium concentration (mg/L) for a sample of cows given a selenium supplement (the treatment group) and a control sample given no supplement, both initially and after a 9-day period. Initial Measurement Treatment Control 11.4 9.1 9.6 8.7 10.1 9.7 8.5 10.8 10.2 10.9 10.6 10.6 11.9 10.1 9.9 12.3 10.7 8.8 10.2 10.4 10.3 10.9 11.4 10.4 9.3 11.6 10.6 10.9 10.9 8.3 After 9 Days Treatment Control 138.3 9.2 104 8.9 96.4 8.9 89 10.1 88 9.6 103.8 8.6 147.3 10.4 97.1 12.4 172.6 9.2 146.3 9.5 99 8.4 122.3 8.8 103 12.5 117.8 9.1 121.5 93 (a) Use the given data for the treatment group to determine if…Accumulation of mercury (Hg) in fish is hypothesized to correlate with the fish size. Barbonymus schwanenfeldii is a species commonly found in a dam in Sarawak. Table 1 shows data of Hg concentration (mg/kg) present in three sizes of fish caught in the dam in triplicates. (i, ii, iii was already answered.)