Electricity_Sales Number_of_Customers Price Degree_Days
1,144,781 690,044.7 6.7651 547.4338
1,143,784 693,866.5 6.8928 -26.3267
1,184,600 697,890.9 6.8626 -1.6835
1,139,054 701,234.3 6.2738 12.4116
1,204,495 704,746.5 6.1591 606.3047
1,179,366 709,583.7 6.2017 148.1826
1,085,489 713,389.1 6.5480 -2.0032
1,160,943 717,401.4 5.9404 -83.5602
1,158,592 721,355.7 5.8960 66.9503
1,193,556 724,228.1 6.0853 24.2879
1,202,514 727,191.2 6.2554 -0.9467
1,174,335 729,230.4 6.3808 -56.3871
1,174,335 731,584.4 6.2768 -360.9842
1,161,770 734,456.2 6.5243 -192.4087
1,142,863 737,848.2 6.4216 -2.8573
1,196,627 739,084.7 6.2837 -168.6407
1,236,468 740,332.7 6.1659 551.9068
1,188,673 741,904.4 6.0801 55.7721
1,181,075 743,467.6 6.9015 -2.5041
1,203,114 743,895.9 6.4296 -159.8219
1,168,515 745,209.2 6.9283 -610.3438
1,224,423 748,664.4 6.4846 113.5806
1,417,430 751,690.6 6.2845 1.2786
1,255,205 755,482.9 6.9084 96.0549
1,251,512 758,648.6 6.8695 251.5787
1,245,558 762,147.7 6.3565 29.6604

a. Estimate a regression equation with electricity sales as the dependent variable, using the number of customers and the price as predictor variables. Interpret the coefficients.

Part 2

Multiple regression models with k independent variables have the form shown below, where
β0
is the Y intercept,
βn
is the slope of Y with variable
Xn
when all other variables are held constant, and
εi
is the random error in Y for observation i.

yi=β0+β1x1i+β2x2i+...+βKxKi+εi

Part 3

Notice that this data set has only two independent variables. The multiple regression equation with two independent variables has the form shown below, where
b0,

b1,
and
b2
are the sample regression coefficients of the population parameters
β0,

β1,
and β2.

Yi=b0+b1X1i+b2X2i

Part 4

Use technology to determine a multiple regression equation, rounding to one decimal place. Let
Y
be estimated electricity sales,
X1
be the number of customers, and
X2
be the price.

Y=410,032.1+0.5X1+64,375.8X2

Part 5

Interpret the coefficients of the regression equation.

Regression coefficients in a multiple regression are called net regression coefficients; they estimate the mean change in Y per unit change in a particular X, holding constant the effect of the other X variables. Use the information and the values determined in the previous step to correctly interpret the coefficients of the regression equation.

Part 6

b. Estimate a regression equation (electricity sales) using only number of customers as a predictor variable. Interpret the coefficient and compare the result from part a.

Part 7

Notice that this data set has only one independent variable. The regression equation with one independent variable has the form shown below, where
b0
and
b1
are the sample regression coefficients of the population parameters
β0
and
β1.

Yi=b0+b1X1i

Part 8

Use technology to determine a regression equation, rounding to one decimal place. Let
Y
be estimated electricity sales, and
X1
be the number of customers.

Y=1,072,293+0.2X1

Part 9

Interpret the coefficients of the regression equation.

Regression coefficients in a regression equation are called net regression coefficients; they estimate the mean change in Y per unit change in a particular X. Use the information and the values determined in the previous step to correctly interpret the coefficients of the regression equation.

Part 10

Compare the coefficient for the number of customers found in part a to the coefficient for the number of customers found in part b.

Part 11

The coefficient for the number of customers in part a,
0.5,
is
greater than
the coefficient for the number of customers found in part b,
0.2.

Part 12

c. Estimate a regression equation (electricity sales) using the price and degree days as predictor variables. Interpret the coefficients. Compare the coefficient for price with that obtained in part a.

Part 13

Notice that this data set has only two independent variables. The multiple regression equation with two independent variables has the form shown below, where
b0,

b1,
and
b2
are the sample regression coefficients of the population parameters
β0,

β1,
and β2.

Yi=b0+b1X1i+b2X2i

Part 14

Use technology to determine a multiple regression equation, rounding to one decimal place. Let
Y
be estimated electricity sales,
X1
be the price, and
X2
be the degree days.

Y=905,564.3+48,321.8X1+143.7X2

Part 15

Interpret the coefficients of regression equation.

Regression coefficients in a multiple regression are called net regression coefficients; they estimate the mean change in Y per unit change in a particular X, holding constant the effect of the other X variables. Use the information and the values determined in the previous step to correctly interpret the coefficients of the regression equation.

Part 16
Transcribed Image Text:A company has estimated a regression equation to determine the effect of various predictor variables on the demand for electricity sales. Prepare a series of regression estimates and discuss the results using the quarterly data for electrical sales given in the data table below. Complete parts a through c below. Click the icon to view the data table. a. Estimate a regression equation with electricity sales as the dependent variable, using the number of customers and the price as predictor variables. Interpret the coefficients. Determine the multiple regression equation. Let be estimated electricity sales, X₁ be the number of customers, and X₂ be the price. ý = ( D) + ( D x + (Dx (Type integers or decimals rounded to one decimal place as needed.)

Question

Electricity_Sales Number_of_Customers Price Degree_Days
1,144,781 690,044.7 6.7651 547.4338
1,143,784 693,866.5 6.8928 -26.3267
1,184,600 697,890.9 6.8626 -1.6835
1,139,054 701,234.3 6.2738 12.4116
1,204,495 704,746.5 6.1591 606.3047
1,179,366 709,583.7 6.2017 148.1826
1,085,489 713,389.1 6.5480 -2.0032
1,160,943 717,401.4 5.9404 -83.5602
1,158,592 721,355.7 5.8960 66.9503
1,193,556 724,228.1 6.0853 24.2879
1,202,514 727,191.2 6.2554 -0.9467
1,174,335 729,230.4 6.3808 -56.3871
1,174,335 731,584.4 6.2768 -360.9842
1,161,770 734,456.2 6.5243 -192.4087
1,142,863 737,848.2 6.4216 -2.8573
1,196,627 739,084.7 6.2837 -168.6407
1,236,468 740,332.7 6.1659 551.9068
1,188,673 741,904.4 6.0801 55.7721
1,181,075 743,467.6 6.9015 -2.5041
1,203,114 743,895.9 6.4296 -159.8219
1,168,515 745,209.2 6.9283 -610.3438
1,224,423 748,664.4 6.4846 113.5806
1,417,430 751,690.6 6.2845 1.2786
1,255,205 755,482.9 6.9084 96.0549
1,251,512 758,648.6 6.8695 251.5787
1,245,558 762,147.7 6.3565 29.6604

a. Estimate a regression equation with electricity sales as the dependent variable, using the number of customers and the price as predictor variables. Interpret the coefficients.

Part 2

Multiple regression models with k independent variables have the form shown below, where

β0

is the Y intercept,

βn

is the slope of Y with variable

Xn

when all other variables are held constant, and

εi

is the random error in Y for observation i.

yi=β0+β1x1i+β2x2i+...+βKxKi+εi

Part 3

Notice that this data set has only two independent variables. The multiple regression equation with two independent variables has the form shown below, where

b0,

b1,

and

b2

are the sample regression coefficients of the population parameters

β0,

β1,

and β2.

Yi=b0+b1X1i+b2X2i

Part 4

Use technology to determine a multiple regression equation, rounding to one decimal place. Let

Y

be estimated electricity sales,

X1

be the number of customers, and

X2

be the price.

Y=410,032.1+0.5X1+64,375.8X2

Part 5

Interpret the coefficients of the regression equation.

Regression coefficients in a multiple regression are called net regression coefficients; they estimate the mean change in Y per unit change in a particular X, holding constant the effect of the other X variables. Use the information and the values determined in the previous step to correctly interpret the coefficients of the regression equation.

Part 6

b. Estimate a regression equation (electricity sales) using only number of customers as a predictor variable. Interpret the coefficient and compare the result from part a.

Part 7

Notice that this data set has only one independent variable. The regression equation with one independent variable has the form shown below, where

b0

and

b1

are the sample regression coefficients of the population parameters

β0

and

β1.

Yi=b0+b1X1i

Part 8

Use technology to determine a regression equation, rounding to one decimal place. Let

Y

be estimated electricity sales, and

X1

be the number of customers.

Y=1,072,293+0.2X1

Part 9

Interpret the coefficients of the regression equation.

Regression coefficients in a regression equation are called net regression coefficients; they estimate the mean change in Y per unit change in a particular X. Use the information and the values determined in the previous step to correctly interpret the coefficients of the regression equation.

Part 10

Compare the coefficient for the number of customers found in part a to the coefficient for the number of customers found in part b.

Part 11

The coefficient for the number of customers in part a,

0.5,

is

greater than

the coefficient for the number of customers found in part b,

0.2.

Part 12

c. Estimate a regression equation (electricity sales) using the price and degree days as predictor variables. Interpret the coefficients. Compare the coefficient for price with that obtained in part a.

Part 13

Notice that this data set has only two independent variables. The multiple regression equation with two independent variables has the form shown below, where

b0,

b1,

and

b2

are the sample regression coefficients of the population parameters

β0,

β1,

and β2.

Yi=b0+b1X1i+b2X2i

Part 14

Use technology to determine a multiple regression equation, rounding to one decimal place. Let

Y

be estimated electricity sales,

X1

be the price, and

X2

be the degree days.

Y=905,564.3+48,321.8X1+143.7X2

Part 15

Interpret the coefficients of regression equation.

Regression coefficients in a multiple regression are called net regression coefficients; they estimate the mean change in Y per unit change in a particular X, holding constant the effect of the other X variables. Use the information and the values determined in the previous step to correctly interpret the coefficients of the regression equation.

Part 16

A company has estimated a regression equation to determine the effect of various predictor variables on the demand for
electricity sales. Prepare a series of regression estimates and discuss the results using the quarterly data for electrical
sales given in the data table below. Complete parts a through c below.
Click the icon to view the data table.
a. Estimate a regression equation with electricity sales as the dependent variable, using the number of customers and
the price as predictor variables. Interpret the coefficients.
Determine the multiple regression equation. Let be estimated electricity sales, X₁ be the number of customers, and
X₂ be the price.
ý = ( D) + ( D x + (Dx
(Type integers or decimals rounded to one decimal place as needed.)

Accepted Answer

As per our guidelines I can solve only first 3 subparts. Kindle post the remaining subparts again…