Solution-Best fit line in scatter plot of regression

Best fit line in scatter plot of regression analysis

Assignment Help Basic Statistics

Reference no: EM13924280

Part I:

1. How would you define "the best fit line" in scatter plot of regression analysis?

a. An imaginary line drawn in such a way that the total variance of distance for each data point from this line is minimized.
b. An imaginary line drawn in such a way that the total variance of distance for each data point from this line is maximized.
c. An imaginary line drawn in such a way that the total variance of distance for each data point from this line remains constant.
d. All of the above.

2. In order to run a linear regression, the following assumption(s) have to be met:

a. Data fits the straight line model
b. Both, the DV and IV(s) have to be continuous variables
c. Both "a" and "b"
d. None of the above

3. R Square is a measure of

a. Residual's in DV explained by the IV(s) in regression analysis
b. Regression's in DV explained by the IV(s) in regression analysis
c. Variance explained in DV by the IV(s) in regression analysis
d. All of the above

4. If the "F" value in ANOVA table of Linear Regression Analysis is significant (p < .05), what does it mean?

a. The data does not fit the straight line model
b. The data fits the curvilinear model
c. The data does not fit the curvilinear model
d. The data fits the straight line model
e. All of the above

5. If the "F" value in ANOVA table of Linear Regression Analysis is not significant (p > .05), what does it mean?

a. The data does not fit the straight line model
b. We cannot proceed with Regression Analysis
c. The data fits the straight line model
d. We can proceed with Regression Analysis
e. Both "a" and "b"

6. In the equation for a straight line y = a + bx, the intercept "a" is

a. the dependent variable
b. the variable used to predict the dependent variable
c. the change in y for any unit change in x
d. the distance from origin to the point where the straight line cuts the y axis, at x = 0

7. In the formula for a straight line y = a + bx, the slope "b" is defined as

a. the change in y for a unit change in x
b. where the line cuts the y axis when x = 0
c. the variable used to predict the dependent variable
d. the dependent variable

8. If the intercept (constant) is found to be 2 and the slope is found to be 5, for any independent variable X in a Bivariate Regression coefficient table results, and are found to be significant, then the equation will be given by (where Y is the dependent variable):

a. Y = 2 + 3X
b. Y = 2 + 5X
c. Y = 5 + 2X
d. Y = 3 + 2X

9. In a multiple regression, the relative importance of the independent variables in predicting/explaining the dependent variable is determined by examining the:

a. R2 values
b. F-values
c. unstandardized (B) values
d. p values

10. Multiple Regression analysis there is/are ________ independent variable(s) and _____ dependant variable(s).

a. One: more than one
b. More than one: one
c. Nonmetric-scaled: metric scaled
d. Multiple: multiple
e. One: multiple

Part II:

Regression (visitfre(DV), prices(IV)
Variables Entered/Removeda
Model Variables Entered Variables Removed Method

1 pricesb . Enter

a. Dependent Variable: visitfre
b. All requested variables entered.
Model Summary
Model R R Square Adjusted R Square Std. Error of the Estimate
1 .160a .026 .017 1.088
a. Predictors: (Constant), prices

ANOVAa
Model Sum of Squares df Mean Square F Sig.
1 Regression 3.668 1 3.668 3.099 .081b
Residual 139.657 118 1.184
Total 143.325 119
a. Dependent Variable: visitfre
b. Predictors: (Constant), prices
Coefficientsa
Model Unstandardized Coefficients Standardized Coefficients t Sig.
B Std. Error Beta
1 (Constant) 2.773 .383 7.237 .000
prices .176 .100 .160 1.761 .081
a. Dependent Variable: visitfre

11. In the SPSS Tables Set-1 for the Regression Analysis, what is the dependent variable and what is/are the independent variable(s) respectively:

a. visitfre and prices
b. price and visitfre
c. visitfre and location
d. location and prices

12. In the SPSS Tables Set-1 for the Regression Analysis, what % of variance in visitfre is explained by prices. (Hint- Look for R-Square value as a % of 1)

a. 16.0%
b. 2.6%
c. 8.1%
d. 10.0 %
13. In the SPSS Tables Set-1 for the Regression Analysis, does the data fits the straight line model (Hint- look at the significance of "F" value in ANOVA table).

a. Yes, we can proceed with regression analysis
b. No, we cannot proceed with regression analysis

Part III:

Regression (visitfre(DV), entertai(IV)
Variables Entered/Removeda
Model Variables Entered Variables Removed Method
1 entertaib . Enter
a. Dependent Variable: visitfre
b. All requested variables entered.

Model Summary
Model R R Square Adjusted R Square Std. Error of the Estimate
1 .427a .182 .175 .997
a. Predictors: (Constant), entertai

ANOVAa
Model Sum of Squares df Mean Square F Sig.
1 Regression 26.145 1 26.145 26.328 .000b
Residual 117.180 118 .993
Total 143.325 119
a. Dependent Variable: visitfre
b. Predictors: (Constant), entertai

Coefficientsa
Model Unstandardized Coefficients Standardized Coefficients t Sig.
B Std. Error Beta
1 (Constant) 1.772 .335 5.294 .000
entertai .451 .088 .427 5.131 .000
a. Dependent Variable: visitfre

14. In the SPSS Tables Set-2 for the Regression Analysis, what is the dependent variable and what is/are the independent variable(s) respectively:

a. visitfre and prices
b. price and visitfre
c. visitfre and entertai
d. location and prices

15. In the SPSS Tables Set-2 for the Regression Analysis, what % of variance in visitfre is explained by entertai. (Hint- Look for R-Square value as a % of 1)

a. 16.0%
b. 2.6%
c. 18.2%
d. 10.0 %

16. In the SPSS Tables Set-2 for the Regression Analysis, does the data fits the straight line model (Hint- look at the significance of "F" value in ANOVA table).

a. Yes, we can proceed with regression analysis
b. No, we cannot proceed with regression analysis

Part IV:

Variables Entered/Removeda
Model Variables Entered Variables Removed Method
1 beconvie, entertai, feelsafeb . Enter
a. Dependent Variable: visitfre
b. All requested variables entered.
Model Summary
Model R R Square Adjusted R Square Std. Error of the Estimate
1 .591a .350 .333 .896
a. Predictors: (Constant), beconvie, entertai, feelsafe
ANOVAa
Model Sum of Squares df Mean Square F Sig.
1 Regression 50.114 3 16.705 20.788 .000b
Residual 93.211 116 .804
Total 143.325 119
a. Dependent Variable: visitfre
b. Predictors: (Constant), beconvie, entertai, feelsafe

Coefficientsa
Model Unstandardized Coefficients Standardized Coefficients t Sig.
B Std. Error Beta
1 (Constant) .318 .416 .763 .447
entertai .345 .081 .327 4.237 .000
feelsafe .191 .093 .170 2.043 .043
beconvie .287 .075 .320 3.830 .000
a. Dependent Variable: visitfre

17. In the SPSS Tables Set-3 for the Regression Analysis, what is the dependent variable and what is/are the independent variable(s) respectively:

a. visitfre and prices, location, foodtype
b. price and visitfre, entertain, beconvie
c. visitfre and entertain, feelsafe, beconvie
d. location and prices, entertain, feelsafe

18. In the SPSS Tables Set-3 for the Regression Analysis, what % of variance in DV (visitfre) is explained by the IV(s). (Hint- Look for R-Square value as a % of 1)

a. 59.1%
b. 2.6%
c. 18.2%
d. 35.0 %

19. In the SPSS Tables Set-3 for the Regression Analysis, does the data fits the straight line model (Hint- look at the significance of "F" value in ANOVA table).

a. Yes, we can proceed with regression analysis
b. No, we cannot proceed with regression analysis

20. In the SPSS Tables Set-3 for the Regression Analysis, when running a linear regression to find out the impact of "entertain", "feelsafe", and "beconvie" (ALL TAKEN TOGETHER) on "visitfre" , what is the regression equation in form of y = c + m1x1 + m2x2 + m3x3 (where y-visitfre, c-constant, x1-entertai, m1-slope of entertai, x2-feelsafe, m2-slope of feelsafe, x3-beconvie, and m3- slope of beconvie) depicting this relationship. (Hint- Look at respective values of unstandardized coefficients in the coefficients table)

a. y = 1.792 + 0.414x1 + 0.411x2 + 0.411x3
b. y = 0.318 + 0.345x1 + 0.191x2 + 0.287x3
c. y = 0.381 + 0.099x1 + 0.079x2 + 0.411x3
d. y = 0.127 + 0.162x1 + 0.210x2 + 0.507x3

21. The coefficient of correlation ranges from -1 to +1, what is the range of "unstandardized B weight" or the slope for any independent variable in regression analysis?

a. -1 to +1
b. -10 to +10
c. -∞ to +∞
d. -100 to +100

22. Assuming any two variables' have a perfect positive CORRELATION of +1 and the SLOPE of the best fit line in Bivariate Regression for some other set of a DV and an IV is found to be +1. What happens to the value of correlation and slope if, by including some more data, the angle of inclination of the lines in correlation and regression increases from the prior 45 degrees.

a. Correlation Decreases / Slope Increases
b. Correlation Increases / Slope Increases
c. Correlation Decreases / Slope Decreases
d. Correlation Increases / Slope Decreases

Reference no: EM13924280

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Best fit line in scatter plot of regression analysis

Reference no: EM13924280

Reference no: EM13924280

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