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- Find the equation of the regression line for the following data set. x 1 2 3 y 0 3 4Olympic 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 following fictitious table shows kryptonite price, in dollar per gram, t years after 2006. t= Years since 2006 0 1 2 3 4 5 6 7 8 9 10 K= Price 56 51 50 55 58 52 45 43 44 48 51 Make a quartic model of these data. Round the regression parameters to two decimal places.
- The table presents data on the taste test of 38 brands of pinot noir wine [data were first reported in an article by Kwan, Kowalski, and Skogenboe in the Journal Agricultural and Food Chemistry (1979, Vol. 27), the response variable is y = quality, and we want to find the "best" regression equation that relates quality to the other five parametersThe 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.And run a simple linear regression in SPSS to determine if pulse at warm-up (The name of the variable in SPSS is "stage 1" and its label is "pulse at warmup") significantly predicts pulse while running ( The name of the variable in SPSS is "stage 3" and its label is "pulse running"). Use α = .05 Is the regression equation significant? That is, does pulse at warm-up explains (or predicts) a significant amount of variability in pulse while running? Report the F, df (of numerator, and df of the denominator) and p-value.
- 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 table below contains the geographic latitudes, x, and average January temperatures, y, of 20 cities. Use Excel to find the best fit linear regression equation. Round the slope and intercept to two decimal places. x y46 2332 6039 4033 5938 5740 3342 3330 6434 5641 3936 4939 5447 2026 7645 2531 6239 4243 3137 5541 31 Answer: y=___x+___
- The table contains data on vehicle speed (h) and fuel consumption (lt / 100km) of 5 randomly selected vehicles. Estimate the average fuel consumption of a vehicle traveling at 45 km / h using the simple linear regression equation between vehicle speed and fuel consumption. Speed 55 60 65 70 75 Consumption 13 12 11 10 9 a. 15 b. 8 c. 7 d. 20The table below contains the geographic latitudes, x, and average January temperatures, y, of 20 cities. Use Excel to find the best fit linear regression equation. Round the slope and intercept to two decimal places. x y 46 23 32 60 39 40 33 59 38 57 40 33 42 33 30 64 34 56 41 39 36 49 39 54 47 20 26 76 45 25 31 62 39 42 43 31 37 55 41 31The estimated regression equation for a model involving two independent variables and 10 observations follows. Y=25.7067 + 0.2795x1 + 0.7337x2 A. Interpret b1 and b2 in this estimated trgression equation. B1 = ? B2 = ? Thank you