O The related coefficient of determination is 0.1 O All of the other answers are true O Only 10% of the variation of the ice-cream sales is explained by different outdoor temperatures. O c in the linear regression mode Y = b + cX is positive O 90% of the variation of the ice-cream sales is due to the variance of the sales itself.
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Q: O None of the other answers O 0.3174 O 0.1587 O 0.8413 O 0.3413
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Question 27
In March, Maggie collected the daily sales of ice-cream in Montreal (Y) and the outdoor temperature for each day (X). She computed the sample
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- Find the equation of the regression line for the following data set. x 1 2 3 y 0 3 4For the following exercises, consider this scenario: The profit of a company decreased steadily overa ten-year spam.The following ordered pairs shows dollars and the number of units sold in hundreds and the profit in thousands ofover the ten-year span, (number of units sold, profit) for specific recorded years: (46,600),(48,550),(50,505),(52,540),(54,495). Use linear regression to determine a function Pwhere the profit in thousands of dollars depends onthe number of units sold in hundreds.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.
- bThe average rate of change of the linear function f(x)=3x+5 between any two points is ________.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?For the following exercises, consider the data in Table 5, which shows the percent of unemployed in a city ofpeople25 years or older who are college graduates is given below, by year. 41. Based on the set of data given in Table 7, calculatethe regression line using a calculator or othertechnology tool, and determine the correlationcoefficient to three decimal places.
- In a statistics course, a linear regression equation was computed to predict the final exam score from the score on the midterm exam. The equation of the least‑squares regression line was ?̂ =10+0.9?,y^=10+0.9x, where ?y represents the final exam score and ?x is the midterm exam score. Suppose Joe scores an 80 on the midterm exam. What would be the predicted value of his score on the final exam?A recent study showed that the hours a person exercised in a week affected the individual'sresting heart rate. It was computed that r = -.68 and the least squares regression line was?̂ = 83-1.4x, where x is the hours exercised and y is the resting heart rate. d. What percentage of variability in resting heart rate can be explained by variability inhours exercised?A recent study showed that the hours a person exercised in a week affected the individual'sresting heart rate. It was computed that r = -.68 and the least squares regression line was?̂ = 83-1.4x, where x is the hours exercised and y is the resting heart rate. c. What does the value -1.4 tell you about the relationship between hours exercisedresting heart rate?
- Suppose the Sherwin-Williams Company has developed the following multiple regression model, with paint sales Y (x 1,000 gallons) as the dependent variable and promotional expenditures A (x $1,000) and selling price P (dollars per gallon) as the independent variables. Y=α+βaA+βpP+ε�=�+���+���+� Now suppose that the estimate of the model produces following results: α=344.585�=344.585, ba=0.106��=0.106, bp=−12.112��=−12.112, sba=0.155�ba=0.155, sbp=4.312�bp=4.312, R2=0.764�2=0.764, and F-statistic=12.593F-statistic=12.593. Note that the sample consists of 10 observations. According to the estimated model, holding all else constant, a $1,000 increase in promotional expenditures sales by approximately gallons. Similarly, a $1 increase in the selling price sales by approximately gallons. Which of the independent variables (if any) appears to be statistically significant (at the 0.05 level) in explaining paint sales? Check all that apply. Selling price (P)…Suppose the Sherwin-Williams Company has developed the following multiple regression model, with paint sales Y (x 1,000 gallons) as the dependent variable and promotional expenditures A (x $1,000) and selling price P (dollars per gallon) as the independent variables. Y=α+βaA+βpP+εY=α+βaA+βpP+ε Now suppose that the estimate of the model produces following results: α=344.585α=344.585, ba=0.102ba=0.102, bp=−11.192bp=−11.192, sba=0.173sba=0.173, sbp=4.487sbp=4.487, R2=0.813R2=0.813, and F-statistic=11.361F-statistic=11.361. Note that the sample consists of 10 observations. 1.)The given F-value shows that you cannot or can reject the null hypothesis that neither one of the independent variables explain a significant (at the 0.05 level) proportion of the variation in income. 2.)Based on the regression model, what is the best estimate of paint sales (x 1,000 gallons) in a sales region where promotional expenditures are $110,000and the selling price is $12.50? a.)213.792…Which of the following statements is true with respect to a simple linear regression model? The percent of variation in the dependent variable that is explained by the regression model is equal to the square of the correlation coefficient between the x and y variables If the correlation coefficient between the x and y variables is negative, the sign on the regression slope coefficient will also be negative If the correlation between the dependent and the independent variable is determined to be significant, the regression model for y given x will also be significant All of the above are true