Given n data pairs, (x₁, y₁),... (xn, Yn), the values of the two constants in the least squares straight-line regression model yao + a₁x are unique. O True False
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A: Introduction - Coefficient of determination Formula r=n∑xy-∑x∑yn∑x2-∑x2n∑y2-∑y2
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![Given n data pairs, (x₁, y₁),... (xn, Yn),
the values of the two constants in the least
squares straight-line regression model
y = ao + a₁x are unique.
O True
O False](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F22d73ce5-1959-43c7-8f97-817be74d23a0%2F9f225fd7-1973-42a7-8b1b-1cecdb6ac788%2Fu8bbmv_processed.jpeg&w=3840&q=75)
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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?Cellular Phone Subscribers The table shows the numbers of cellular phone subscribers y in millions in the United States from 2008 through 2013. Source: CTIA- The Wireless Association Year200820092010201120122013Number,y270286296316326336 (a) Find the least squares regression line for the data. Let x represent the year, with x=8 corresponding to 2008. (b) Use the linear regression capabilities of a graphing utility to find a linear model for the data. How does this model compare with the model obtained in part a? (c) Use the linear model to create a table of estimated values for y. Compare the estimated values with the actual data.The table shows the numbers of new-vehicle sales (in thousands) in the United States for Company A and Company B for 10 years. The equation of the regression line is ModifyingAbove y with caret equals 0.993 x plus 1 comma 195.82y=0.993x+1,195.82. Complete parts (a) and (b) below. New-vehicle sales left parenthesis Company Upper A right parenthesis comma x(Company A), x 4 comma 1674,167 3 comma 8823,882 3 comma 5693,569 3 comma 4433,443 3 comma 2993,299 3 comma 1173,117 2 comma 8372,837 2 comma 4982,498 1 comma 9401,940 2 comma 0842,084 New-vehicle sales left parenthesis Company Upper B right parenthesis comma y(Company B), y 4 comma 9204,920 4 comma 8444,844 4 comma 8374,837 4 comma 7104,710 4 comma 6754,675 4 comma 4284,428 4 comma 6604,660 3 comma 8323,832 2 comma 9272,927 2 comma 7532,753 Question content area bottom Part 1 (a) Find the coefficient of determination and interpret the result.…
- If the points (x1, y1), (x2, y2),..., (xn, yn) lie on a straight line, what can you say about the regression line associated with these points?The manufacturer of Beanie Baby dolls used quarterly price data for 2012/- 2020/V (t = 1, ..., 36) and the regression equation Pt = a + bt + c₁D1 t + c2 D2t + c3D3 t to forecast doll prices in the year 2021. Pt is the quarterly price of dolls, and D1, D2t, and D3 are dummy variables for quarters I, II, and III, respectively. DEPENDENT VARIABLE: PT R-SQUARE P-VALUE ON F 0.0001 OBSERVATIONS: 36 0.9078 F-RATIO 76.34 STANDARD ERROR PARAMETER ESTIMATE T-RATIOP-VALUE VARIABLE INTERCEPT 24.0 6.20 3.87 0.0005 T 0.8 0.240 3.33 0.0022 D1 -8.0 2.60 -3.08 0.0043 D2 -6.0 1.80 -3.33 0.0022 D3 -4.0 0.60 -6.67 0.0001 In any given year price tends to vary from quarter to quarter as follows: Multiple Choice O O O P₁ > P|| > P||| > PIV PI> PIV> Pill > PII Pll > Pill > PIV> PI Pill > PI>PII > PIV PIV> Pill > PII > PIUse the general equation for the least square regression line to show that this line always passes through the point (x,y) * bars above the x and y.That is, set x=x(with a bar above the x) and show that the line predicts that y=y (with a bar above the y).
- Suppose there is 1 dependent variable (dissolved oxygen, Y) and 3 independent variables (water temp X1, depth X2, and hardness of water X3). Below is the result of the multiple linear regression.Which of the following is the equation of the multiple regression model? Y = 4.36 + 0.37X1 + 0.24X2 + 0.04X3 Y = 0.00 + 0.02X1 + 0.56X2 + 0.37X3 Y = 24.84 - 1.17X1 - 0.15X2 - 0.04X3 Y = 5.69 – 3.20X1 - 0.61X2 -0.95X3ASAPThe manufacturer of Beanie Baby dolls used quarterly price data for 2012/-2020/V (t = 1, ..., 36) and the regression equation Pt= a + bt+c₁D1 t + c2 D2 + + c3 D3 t to forecast doll prices in the year 2021. Pt is the quarterly price of dolls, and D1, D2t, and D3+ are dummy variables for quarters I, II, and III, respectively. DEPENDENT VARIABLE: PT R-SQUARE P-VALUE ON F 0.0001 OBSERVATIONS: F-RATIO 76.34 STANDARD 36 0.9078 PARAMETER VARIABLE ESTIMATE ERROR T-RATIOP-VALUE INTERCEPT 24.0 6.20 3.87 0.0005 T 0.8 0.240 3.33 0.0022 D1 -8.0 2.60 -3.08 0.0043 D2 -6.0 1.80 -3.33 0.0022 D3 -4.0 0.60 -6.67 0.0001 The estimated quarterly increase in price is and the estimated annual increase in price is Multiple Choice O O $1.50; $6.00 $1.40; $4.00 $0.60; $2.40 $0.80; $3.20 None of the choices are correct.
- 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 11 10 9 8 7 Please choose one: a. 6 b. 5 c. 13 D. 8Consider the two variable regression model: Y = Bo+P,Edu+ B2EXP21 + u, where Y denotes the average monthly income, Edu denotes the number of years of education, Exp denotes the number of years of experience, and u, denotes the error term. Suppose the researcher wants to test whether the effect of education on average monthly income and the effect of experience on the average monthly income of an individual are the same or not So, the test the researcher wants to conduct is Ho: B = 6, vs. H, f,+P2 The hypotheses can be tested by modifying the original regression equation to turn the restriction into a restriction on a single regression coefficient. Suppose the regression function is modified in the following way: Y, Po+Y,Edu, + B2W +u, where y, =P,-P2 and W, = Edu,, + Exp2i %D Since y, = B, - B2, the test the researcher wants to conduct will now be Ho: y=0 vs. H y0. Let y, and SE(y,), denote the estimated slope coefficient of y, and the standard error of 7, respectively. is .D IS If…Consider the linear regression model Y; = Bo + B1 X¡ + U¡ for each i in $10,000) and Y; represents the home size (measured in square feet). We run an OLS regression and get: 1,..., n withn = 1,000. X; represents the annual income of individual i (measured Bin = 43.2, SE(§ „) = 10.2, Bon = 700, SE(Bom) = 7.4. Suppose that we want to test Ho : B1 O against H1 : ß1 # 0 at 1% significance level. Assuming that the sample size is large enough, which one of the following is true about the p-value of this test? 43.2 The p-value can be computed as P(-| ), where is the standard Normal CDF 10.2 а. b. None of the answers 43.2 The p-value can be computed as (- ), where O is the standard Normal CDF 10.2 С. 43.2 d. The p-value can be computed as 20(-- ), where O is the standard Normal CDF 10.2
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