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Regression line
x1 = 1.5 + 3.6x2 -7.7x3 + 2.3x4
a)
Response variable = x1
Explanatory variables = x2,x3,x4
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- Find the equation of the regression line for the following data set. x 1 2 3 y 0 3 4The population P (in millions) of Texas from 2001 through 2014 can be approximated by the model P=20.913e0.0184t, where t represents the year, with t=1 corresponding to 2001. According to this model, when will the population reach 32 million?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.
- Use the following linear regression equation to answer the questions. x1 = 1.7 + 3.9x2 – 8.5x3 + 2.2x4 Which variables are the explanatory variables? (Select all that apply.) x2x4x1x3 (b) Which number is the constant term? List the coefficients with their corresponding explanatory variables. constant ? x2 coefficient ? x3 coefficient ? x4 coefficient ? (c) If x2 = 6, x3 = 7, and x4 = 4, what is the predicted value for x1? (Use 1 decimal place.) Suppose x3 and x4 were held at fixed but arbitrary values and x2 increased by 1 unit. What would be the corresponding change in x1? Suppose x2 increased by 2 units. What would be the expected change in x1? Suppose x2 decreased by 4 units. What would be the expected change in x1? (e) Suppose that n = 18 data points were used to construct the given regression equation and that the standard error for the coefficient of x2 is 0.454. Construct a 99% confidence interval for the coefficient of x2. (Use 2 decimal places.) lower limit ?…Use the following linear regression equation to answer the questions. x1 = 1.5 + 3.6x2 – 7.8x3 + 1.8x4(a) Which variable is the response variable? answer: x1 Which variables are the explanatory variables? (Select all that apply.) answer: x4x3x2 (b) Which number is the constant term? List the coefficients with their corresponding explanatory variables. constant 1.5 x2 coefficient 3.6 x3 coefficient -7.8 x4 coefficient 1.8 (c) If x2 = 10, x3 = 7, and x4 = 7, what is the predicted value for x1? (Use 1 decimal place.) answer: -4.5 (d) Explain how each coefficient can be thought of as a "slope" under certain conditions. answer: If we hold all other explanatory variables as fixed constants, then we can look at one coefficient as a "slope." Suppose x3 and x4 were held at fixed but arbitrary values and x2 increased by 1 unit. What would be the corresponding change in x1? answer: 3.6 Suppose x2 increased by 2 units. What would be the expected change in x1? answer: 7.2 Suppose…Use the following linear regression equation to answer the questions. x3 = −16.2 + 4.5x1 + 10.0x4 − 1.4x7 Which variables are the explanatory variables? (Select all that apply.) x7x4x3x1 (b) Which number is the constant term? List the coefficients with their corresponding explanatory variables. constant x1 coefficient x4 coefficient x7 coefficient (c) If x1 = 6, x4 = -2, and x7 = 4, what is the predicted value for x3? (Round your answer to one decimal place.)x3 =
- Use the following linear regression equation to answer the questions. x1 = 2.0 + 3.6x2 – 7.8x3 + 2.1x4 a) Which variables are the explanatory variables? (Select all that apply.) x3 x1 x2 x4 (b) Which number is the constant term? List the coefficients with their corresponding explanatory variables. constant _____ x2 coefficient _____ x3 coefficient _____ x4 coefficient ______ (c) If x2 = 9, x3 = 3, and x4 = 6, what is the predicted value for x1? (Use 1 decimal place.)Use the following linear regression equation to answer the questions. X3=-17.3+3.7x1+9.6x4-2.0x7 a) which number is the constant term? List the coefficient explanatory variables. constant= x1 coefficient = x4 coefficient =x7 coefficient =b) if x1=1, x4=-3, x7=5, what is the predicted value for x3?(round you answer to one decimal place.) c) suppose x1 and x7 were held at fixed but arbitrary values. If x4 increased by 1 unit what would we expect the corresponding change in x3 to be? if x4 increased by 3 units what would be the corresponding expected change in x3?if x4 decreased by 2 units what would we expect for the corresponding change in x3?Use the following linear regression equation to answer the questions. x1 = 1.5 + 3.6x2 – 7.8x3 + 1.8x4 Which variables are the explanatory variables? (Select all that apply.) x4x3x2x1 (c) If x2 = 10, x3 = 7, and x4 = 7, what is the predicted value for x1? (Use 1 decimal place.)Suppose x3 and x4 were held at fixed but arbitrary values and x2 increased by 1 unit. What would be the corresponding change in x1?Suppose x2 increased by 2 units. What would be the expected change in x1?Suppose x2 decreased by 4 units. What would be the expected change in x1?(e) Suppose that n = 13 data points were used to construct the given regression equation and that the standard error for the coefficient of x2 is 0.461. Construct a 95% confidence interval for the coefficient of x2. (Use 2 decimal places.) lower limit upper limit (f) Using the information of part (e) and level of significance 1%, test the claim that the coefficient of x2 is different from zero. (Use 2 decimal places.) t t…
- Use the following linear regression equation to answer the questions. x3 = −17.3 + 4.1x1 + 9.6x4 − 1.6x7 Suppose x1 and x7 were held at fixed but arbitrary values. a) If x4 increased by 1 unit, what would we expect the corresponding change in x3 to be? b) If x4 increased by 3 units, what would be the corresponding expected change in x3? c) If x4 decreased by 2 units, what would we expect for the corresponding change in x3?Use the following linear regression equation to answer the questions. x3 = −15.4 + 4.0x1 + 8.2x4 − 1.2x7 (d)Suppose x1 and x7 were held at fixed but arbitrary values.If x4 increased by 1 unit, what would we expect the corresponding change in x3 to be?If x4 increased by 3 units, what would be the corresponding expected change in x3?If x4 decreased by 2 units, what would we expect for the corresponding change in x3?(e) Suppose that n = 14 data points were used to construct the given regression equation and that the standard error for the coefficient of x4 is 0.917. Construct a 90% confidence interval for the coefficient of x4. (Round your answers to two decimal places.) lower limit upper limit (f) Using the information of part (e) and level of significance 5%, test the claim that the coefficient of x4 is different from zero. (Round your answers to two decimal places.) t = t critical = ±student obtained the following two regression equations. Do you agree with him? (1) 6X=15Y+21, (ii) 21X+14Y=56