Question

This is all one problem, please solve completely. Thank you.

some association On-Line Discount Broker Survey polls members on their experiences with discount brokers. As part of the survey, members were asked to rate the quality of the speed of execution with their broker as well as provide an overall satisfaction rating for electronic trades. Possible responses (scores) were no opinion (0), unsatisfied (I), somewhat satisfied (2), satisfied (3) and very satisfied (4). For each broker summary scores were computed by calculating a weighted average f the scores provided by each respondent. A portion the survey results follow Brokerage Speed Satisfaction Scottrade, Inc 3.3 3.8 Charles Schwab 4.0 3.6 Fidelity Brokerage Services 3.4 3.2 TD Ameritrade 3.9 4.0 E'Trade Financial 2,5 2,5 Vanguard Brokerage Services 3.4 3.5 2.6 2,7 USAA Brokerage Services Thinkorswim 3.6 4.0 Wells Fargo Investments 4,0 3.8 Interactive Brokers 3,6 3,5 Zecco.com 2.6 2,8 a. Select a scatter diagram for these data with the speed of execution as the independent variable. A. B. 4.5 4.5 3.5 3.5 3 2.5+ 2.5- 2.5 3.5 4 4.5 2.5 3.5 4 4.5 Speed of Exec ution Speed of Exec ution Satisfaction Satistaction C D. 4,5 4,5- H 3 2.5 2.5 2.5 4,5 2,5 4,5 3 3.5 3 3.5 Speed of Exec ution Speed of Exec ution -Select your answer Sat isfaction Satisfaction o. What does the scatter diagram developed in part (a) indicate about the relationship between the two variables? speed of execution rating and y overall satisfaction rating for electronic trades. The scatter diagram indicates a linear relationship between Select vour answer c. Develop the least squares estimated regression equation. Enter negative value as negative number. Speed (to 4 decimals) Satisfaction= the estimated regression equation (to 4 decimals) Provide an interpretation for the slope . So, a one unit - Select your answer - in the speed of execution rating will increase the overall satisfaction rating by The slope of the estimated regression line is approximately approximately points able to increase their speed of execution rating from the current value of 2.5 Suppose ETrade Financial developed new software to increase their speed of execution rating. If the new software execution rating for the other 10 brokerage firms that were surveyed, what value would you predict for the overall satisfaction rating? the average speed (to 3 decimals)

Answer 1

Scatter diagram : option ( B) diagram indicates Positiveline ar D The Scater relation ship betdeem 0 83 45 |Speed Satisfaction O 6003 is The slope of the estimated regression line O 8345 One unit So, a approximately S peed of exe cution vating <dill in the increase overall satisfaction vating by increane the points O.83 45 approximately O. 60030.8 345 (3 44) Predicted overall Satisfaction 3. 409 |

I have calculated all the values through R-STUDIO.

CODE & OUTPUTS:

X_speed <- c(3.3, 4.0, 3.4, 3.9, 2.5, 3.4, 2.6, 3.6, 4.0, 3.6, 2.6)
Y_satisfaction <- c(3.8, 3.6, 3.2, 4.0, 2.5, 3.5, 2.7, 4.0, 3.8, 3.5, 2.8)

plot(X_speed, Y_satisfaction)

corr_coeff <- cor.test(X_speed ,Y_satisfaction ,method="pearson")
print(corr_coeff)

regression_model <- lm(Y_satisfaction ~ X_speed)
summary(regression_model)

X_new_10 <- c(3.3, 4.0, 3.4, 3.9, 3.4, 2.6, 3.6, 4.0, 3.6, 2.6)
summary(X_new_10)

3.0 3.5 2.5 4.0 X_speed C O O O O 0 Y_satisfaction

Pearson's product-moment correlation

data: X_speed and Y_satisfaction
t = 5.6154, df = 9, p-value = 0.0003277
alternative hypothesis: true correlation is not equal to 0
95 percent confidence interval:
0.5991644 0.9691279
sample estimates:
cor
0.8820204

Call:
lm(formula = Y_satisfaction ~ X_speed)

Residuals:
Min 1Q Median 3Q Max
-0.33869 -0.16275 -0.07026 0.10342 0.44552

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 0.6003 0.5048 1.189 0.264803
X_speed 0.8346 0.1486 5.615 0.000328 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.2628 on 9 degrees of freedom
Multiple R-squared: 0.778,   Adjusted R-squared: 0.7533
F-statistic: 31.53 on 1 and 9 DF, p-value: 0.0003277

summary(X_new_10)
Min. 1st Qu. Median Mean 3rd Qu. Max.
2.600 3.325 3.500 3.440 3.825 4.000

~~~~~~~~Thanks~~~~~~~~