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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 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 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
- Consider a simple linear regression model Y=α+βX+ε. We have collected 15 samples, from which we calculated the summary statistics ∑xi=66, ∑x2i=6568, ∑yi=459, ∑y2i=27933, ∑xiyi=11311. Suppose one of the data is supposed to be (x1=10, y1=30), but is incorrectly recorded as (x1=7, y1=34). All other observations are correctly recorded. What is the OLS estimators αˆ= ? and βˆ= ? based on the correct data.A fitted linear regression model is (y=10+2x ). If x = 0 and the corresponding observed value of y = 9, the residual at this observation is:A group of students measure the length and width of a random sample of beans. They are interested in investigating the relationship between the length and width. Their summary statistics are displayed in the table below. All units, if applicable, are millimeters. Mean width: 7.555 Stdev width: 0.914 Mean height: 12.686 Stdev height: 1.634 Correlation coefficient: 0.8203 d) If the students are interested in using the height of the beans to predict the width, calculate the slope of this new regression equation. e) Write the equation of the best-fit line that can be used to predict bean widths. Use x to represent height and y to represent width.
- Consider a linear regression model for the decrease in blood pressure (mmHg) over a four-week period with muy=2.8+0.8x and standard deviation chi=3.2. The explanatory variable x is the number of servings fruits and vegetables in a calorie-controlled diet. Using the 68-95-99.7 rule, between what two values would approximately 95% of the observed responses, y, fall when x = 7?A regression between foot length(response variable in cm) and height (eexplanatory variable in inches) for 33 students resulted in the following regression equation: y^=10,9+0,23X one student in the sample was 73 inches tall with a foot length of 29cm.What is the predicted foot length for A)33cm B)17,57cm C)27,69cm D)29cmhe following estimated regression model was developed relating yearly income (y in $1000s) of 30 individuals with their age (x1) and their gender (x2) (0 if male and 1 if female).ŷ = 30 + 0.7x1 + 3x2Also provided are SST = 1200 and SSE = 384. The yearly income of a 24-year-old female individual is
- The linear regression equation, Y = a + bX, was estimated. The following computer printout was obtained: DEPENDENT VARIABLE: Y R-SQUARE F-RATIO P-VALUE ON F OBSERVATIONS: 18 0.3066 7.076 0.0171 VARIABLE PARAMETER ESTIMATE STANDARD ERROR T-RATIO P-VALUE INTERCEPT 15.48 5.09 3.04 0.0008 X -21.36 8.03 -2.66 0.0171 Given the information in the table, the parameter estimate of b indicatesThe prelim grades (x) and midterm grades (y) of a sample of 10 MMW students is modeled by the regression line y = 12.0623 + 0.7771x. Estimate the prelim grade if the midterm grade is 83.The accompanying data resulted from an experiment in which weld diameter and shear strength (in pounds) were determined for five different spot welds on steel. Below are the data collected and the regression equation. Diameter Strength 200.1 813.7 210.1 785.3 220.1 960.4 230.1 1118.0 240.0 1076.2 Strength = -941.6992 + 8.5988*Diameter The predicted y-hat value for a diameter of 201 is 864. if we observed a weld that had a diameter of 235 that had a strength 1000, what would be its residual?