x:12 21 28 8 20 y:17 15 22 19 24 1. What is the value of...
x:12 21 28 8 20
y:17 15 22 19 24
1. What is the value of b1?
2. What is the value of b0?
3. What is the equation of the y ^ estimator line?
4.if x is increased by 10 units, how much does y ^ change?
5.Assume b0 = 12.953, and b1 = -2.5. For x = 25, predict y
6. How much correlation is there between x and y?
Round to four decimals and use leading zeros if necessary.
7. How much of the variability in y is explained by x?
Round to four decimals and use leading zeros if necessary.
Homework Answers
Use Excel to calculate for the following dataset: X Y 1 10 1 12 3 13...
Use Excel to calculate for the following dataset: X Y 1 10 1 12 3 13 3 17 5 17 5 21 the correlation coefficient: Please round to two decimals the value of the intercept, b0: the value of the slope, b1: the predicted value of Y when X =5:
x 1 11 20 16 19 15 16 10 x2 17 21 17 21 19 21...
x 1 11 20 16 19 15 16 10 x2 17 21 17 21 19 21 14 x3 19 22 21 22 24 23 X4 25 16 17 18 18 x5 26 18 18 22 21 Test at a = 0.10 to determine if the population means are all the same. 1. The null hypothesis is Ho: OM = M2 = M3 = Hy = 45 Oui = ly = H3 = 44 OH = H2 = 43 2. This...
Given are five observations for two variables, x and y. xi 3 12 6 20 14...
Given are five observations for two variables, x and
y.
xi
3
12
6
20
14
yi
50
45
55
15
15
(d) Develop the estimated regression equation by computing the
values of b0 and b1 using b1 =
Σ(xi − x)(yi − y)
Σ(xi − x)2
and b0 = y − b1x.
ŷ =
(e) Use the estimated regression equation to predict the value
of y when x = 9.
Observation 1 2 3 4 5 6 7 8...
For a set of data: x = (0,1,2,3,4,5,6) and y=(36, 28, 25, 24, 23, 21, 19),...
For a set of data: x = (0,1,2,3,4,5,6) and y=(36, 28, 25, 24, 23, 21, 19), is it wise to use a linear regression to extrapolate data for x = 50? Solution: Since the coefficient of determination is 0.8582, the linear model is a reasonably good fit for the data, so extrapolation for any x-value is acceptable. What is wrong with this solution?
A statistical program is recommended. Consider the following data for two variables, x and y. x...
A statistical program is recommended. Consider the following data for two variables, x and y. x 9 32 18 15 26 y 11 19 20 16 22 (a) Develop an estimated regression equation for the data of the form ŷ = b0 + b1x. (Round b0 to two decimal places and b1 to three decimal places.) ŷ = Comment on the adequacy of this equation for predicting y. (Use α = 0.05.) The high p-value and low coefficient of determination...
X: 19 0 34 35 28 30 24 -24 -8 -13 y: 8 -5 24 22...
X: 19 0 34 35 28 30 24 -24 -8 -13 y: 8 -5 24 22 12 26 9 -9 -2 -4 (a) Compute Ex, Ex2, Ey, Ey? Ex 125 Ex2 5811 Ey 81 Ey2 2151 (b) Use the results of part (a) to compute the sample mean, variance, and standard deviation for x and for y. (Round your answers to two decimal places.) 12.5 8.1 s 21.73 12.89 (c) Compute a 75% Chebyshev interval around the mean for x...
A statistical program is recommended. Consider the following data for two variables, x and y. x...
A statistical program is recommended. Consider the following data for two variables, x and y. x 22 24 26 30 35 40 y 13 20 33 35 40 36 (a) Develop an estimated regression equation for the data of the form ŷ = b0 + b1x. (Round b0 to one decimal place and b1 to three decimal places.) ŷ = (b) Use the results from part (a) to test for a significant relationship between x and y. Use α =...
In a study, the protein absorption (Y) for seven concentration levels (X) of that protein were...
In a study, the protein absorption (Y) for seven concentration levels (X) of that protein were measured: Be Specific with answers Conc. Level (Xi) 4 6 8 10 12 14 16 Absorption (Yi) 10 15 18 18 24 22 26 a) Find the least squares estimate for the regression line Yi = b0 + b1Xi+ ei. b) What would be your estimate of the absorption when the concentration level is 10? c) Estimate the standard deviation of the error term...
Questions 21 through 25 refer to the following output: ∑x = 210 ∑x2 = 2870 ∑xy =...
Questions 21 through 25 refer to the following output: ∑x = 210 ∑x2 = 2870 ∑xy = -10745 ∑y = -759 ∑y2 = 62523 Regression Equation: = 5.873684 – 4.173684x Source SS df MS F Regression 11548.06053 1 11584.06053 9.42011 Error 22134.88947 18 1229.716 Total 33718.95 19 21. How many observations were used in the above regression? 1 points QUESTION 22 What percentage of the observed variability in Y is explained by X? 1 points QUESTION 23 What is the...
Using the data file provided with both variables, x and y, answer the following questions using...
Using the data file provided with both variables, x and y, answer the following questions using Excel*: 1.Create a scatterplot with the data. Comment on direction, form, strength, outliers and/or other significant findings. 2.Use the linear model to fit a line to the data and determine the equation ỹ = b0 + b1x and Interpret b0and b1. 3.Calculate the coefficient of correlation. Discuss the strength of correlation between the explanatory and response variables. 4.Predict the value for ỹ when you...
x 1 11 20 16 19 15 16 10 x2 17 21 17 21 19 21 14 x3 19 22 21 22 24 23 X4 25 16 17 18 18 x5 26 18 18 22 21 Test at a = 0.10 to determine if the population means are all the same. 1. The null hypothesis is Ho: OM = M2 = M3 = Hy = 45 Oui = ly = H3 = 44 OH = H2 = 43 2. This...
Given are five observations for two variables, x and
y.
xi
3
12
6
20
14
yi
50
45
55
15
15
(d) Develop the estimated regression equation by computing the
values of b0 and b1 using b1 =
Σ(xi − x)(yi − y)
Σ(xi − x)2
and b0 = y − b1x.
ŷ =
(e) Use the estimated regression equation to predict the value
of y when x = 9.
Observation 1 2 3 4 5 6 7 8...
X: 19 0 34 35 28 30 24 -24 -8 -13 y: 8 -5 24 22 12 26 9 -9 -2 -4 (a) Compute Ex, Ex2, Ey, Ey? Ex 125 Ex2 5811 Ey 81 Ey2 2151 (b) Use the results of part (a) to compute the sample mean, variance, and standard deviation for x and for y. (Round your answers to two decimal places.) 12.5 8.1 s 21.73 12.89 (c) Compute a 75% Chebyshev interval around the mean for x...
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