The Kak Ramah company supplies vegetables to shop as wholesales. The demand for the vegetables depends on the price per kilograms (kg). the data are shown in the following table. Price per 20 22 24 26 28 30 32 kg (RM) Demand 700 685 630 580 515 490 450 (kg) a)By using the linear regression line, calculate the number of sales if the price per kg is RM25 b) Calculate the Pearson correlation value and interpret
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- Olympic Pole Vault The graph in Figure 7 indicates that in recent years the winning Olympic men’s pole vault height has fallen below the value predicted by the regression line in Example 2. This might have occurred because when the pole vault was a new event there was much room for improvement in vaulters’ performances, whereas now even the best training can produce only incremental advances. Let’s see whether concentrating on more recent results gives a better predictor of future records. (a) Use the data in Table 2 (page 176) to complete the table of winning pole vault heights shown in the margin. (Note that we are using x=0 to correspond to the year 1972, where this restricted data set begins.) (b) Find the regression line for the data in part ‚(a). (c) Plot the data and the regression line on the same axes. Does the regression line seem to provide a good model for the data? (d) What does the regression line predict as the winning pole vault height for the 2012 Olympics? Compare this predicted value to the actual 2012 winning height of 5.97 m, as described on page 177. Has this new regression line provided a better prediction than the line in Example 2?The monthly premium quoted by an insurance company for a critical illness policy was collected from a sample of 6 adult male smokers at different age. The data for the sample are shown: Age 28 25 50 39 47 31 Premium ($) 75 40 175 125 250 105 Using Age to predict premium, the Linear Regression equation is given by: ŷ =6.556X−112 and r2=0.813y^=6.556X−112 and r2=0.813 a. Identify the independent and Dependent variables. Dependent: Age Premium Independent: Age Premium b. Determine the slope. Slope = Slope = Round to 3 decimal places c. Determine |r||r| . |r|=|r|= Round to 3 decimal places d. Interpret rr : and e. Determine critical r value at 5% significance level and determine if there is a significant linear correlation exists. |r| critical=|r| critical= Round to 3 decimal places Linear Correlation:Linear Correlation: Significant Not Significant f. Predict the monthly premium for a 40 years old adult male smoker.…The owner of Showtime Movie Theaters, Inc., would like to predict weekly gross revenueas a function of advertising expenditures. Historical data for a sample of eight weeks follow. Weekly GrossRevenue($1000s) Television Advertising($1000s) Newspaper Advertising($1000s) 96 5.0 1.5 90 2.0 2.0 95 4.0 1.5 92 2.5 2.5 95 3.0 3.3 94 3.5 2.3 94 2.5 4.2 94 3.0 2.5 a. Develop an estimated regression equation with the amount of televisionadvertising as the independent variable.b. Develop an estimated regression equation with both television advertising and newspaper advertising as the independent variables. c. Is the estimated regression equation coefficient for television advertisingexpenditures the same in part (a) and in part (b)? Interpret the coefficient in each case. d. Predict weekly gross revenue for a week when $3500 is spent on television advertising and $1800 is spent on newspaper advertising.
- The owner of Original Italian Pizza restaurant chain wants to understand which variable most strongly influences the sales of his specialty deep-dish pizza. He has gathered data on the monthly sales of deep-dish pizzas at his restaurants and observations on other potentially relevant variables for each of several outlets in central Indiana. These data are provided in the file P10_04.xlsx. Estimate a simple linear regression equation between the quantity sold (Y) and each of the following candidates for the best explanatory variable: average price of deep-dish pizzas (X1), monthly advertising expenditures (X2), and disposable income per household in the areas surrounding the outlets (X3). Round your answers for intercept coefficients to the nearest whole number and slope coefficients to two decimal places, if necessary. If your answer is negative number, enter "minus" sign.A medical researcher wishes to determine how the dosage (in milliliters) of an experimental drugaffects the heart rate (in beats per minute) of patients with an elevated heart rate. The data for asample of eight patients with an elevated heart rate are provided in the following table.Drug Dosage 0 5 10 20 25 30 40 50Heart Rate 135 124 106 89 85 72 68 62(a) Determine the linear regression model that will best predict a patient’s heart rate based on thedosage of the drug received. (b) How well does the linear regression model fit this sample data? (c) If a patient with an elevated heart rate is administered a 35 ml dose of this drug, predict theresulting heart rate of the patient.A company that holds the DVD distribution rights to movies previously released only in theaters wants to estimate sales revenue of DVDs based on box office success. The box office gross (in Php millions) for each of 22 movies in the year that they were released and the DVD revenue (in Php millions) in the following year are shown below and stored in a. construct a scatter plot. b. assuming a linear relationship, use the least-squares method to determine the regression coefficients b0 and b c. interpret the meaning of the slope, in this problem d. predict the sales revenue for a movie DVD that had a box office gross of Php75 million..1
- The data regarding the production of wheat in tons (X) and the price of the kilo of flour in Ghana cedis (Y) Takoradi some years ago were: a. Fit the regression line for the day using the method of least squaresA mail-order business selling personal computer supplies, software and hardware maintains a centralized warehouse. Management is currently examining the process of distribution from the warehouse and wants to study the factors that affect the warehouse distribution costs. Data collected over 24 random months contain the warehouse’s distribution cost (in thousands of Rands), the sales (in thousands of Rands) and the number of orders received. A multiple linear regression model was fitted to the data by using Stat1.2. Use the output to answer the questions that follow by typing only the letter of the correct option in the answer boxes. Variablesy: Warehouse Distribution Costx1: Salesx2: Number of Orders Model Fitting StatisticsR2 = 0.8504Adj R2: ? Regression Coefficients Beta Parameter Standard b Parameter Standard Estimates…The table below shows the average weekly wages (in dollars) for state government employees and federal government employees for 10 years. Construct and interpret a 95% prediction interval for the average weekly wages of federal government employees when the average weekly wages of state government employees is $841. The equation of the regression line is ModifyingAbove .y=1.403x+9.259. Wages (state), x 724 747 800 803 839 897 901 939 951 956 Wages (federal), y 1,035 1,060 1,111 1,144 1,190 1,245 1,276 1,306 1,332 1,396 Construct and interpret a 95% prediction interval for the average weekly wages of federal government employees when the average weekly wages of state government employees is $841. Select the correct choice below and fill in the answer boxes to complete your choice. (Round to the nearest cent as needed.) A. There is a 95% chance that the predicted average weekly wages of federal government…
- King & Scott, a research firm for the real estate industry, studied the relation between x=x= annual income (in thousands of dollars) and y=y= sale price of house purchased (in thousands of dollars). A random sample of data was collected from mortgage applications for home sales in the region of the study, and is given in the table. Annual Income House Price 72 188 48 91.6 73 182.2 97 155.5 97 238.8 94 203.4 67 160.1 85 212 64 169 Conduct a linear regression. Use the results to answer the following questions. a. What is the value of the correlation coefficient (round to 3 decimal places)? What does the value tell you about the linear relationship between the annual income and the price of house purchased? Correlation coefficient: This indicates: very weak positive linear correlation fairly strong negative linear correlation perfect positive linear correlation very weak negative linear correlation perfect negative linear correlation no linear…An agronomist undertook an experiment to investigate the factors that potato harvest. In his research, agronomist decided to divide the farm into 30 half hectare plots and apply varies level of fertilizer. Potato was then planted and the harvest at the end of the season was recorded. Fertilizer(Kg) Harvest (tons) 210 43.5 220 40.0 230 48.0 240 65.0 250 80.0 260 85.0 270 95.0 280 80.0 290 97.3 1. Find the simple regression line and interpret the coefficients. 2. Find the coefficient of determination and interpret its value. 3. Does the model appear to be a useful tool in predicting the potato harvest? If so, predict the harvest when 250KG of fertilizer is applied. If not explain why not.The owner of Showtime Movie Theaters, Inc., would like to estimate weekly gross revenue as a function of advertising expenditures. Historical data for a sample of eight weeks follows: Weekly Revenue (£1000s) Television advertising (£1000s) Newspaper advertising (£1000s) 96 5 1.5 90 2 2 95 4 1.5 92 2.5 2.5 95 3 3.3 94 3.5 2.3 94 2.5 4.2 94 3 2.5 a) Calculate the correlation coefficient among the variables and explain the result. b) Plot two simple linear regression equations- i) television advertising as independent variable and weekly revenue as dependent variable ii) newspaper advertising as the independent variable and weekly revenue as dependent variable. You would be using Excel Data Analysis Pack – Regression to get the relationship; c) Create scatter diagrams for each linear relationship and display the linear regression equation and R square value on chart.
