In: Statistics and Probability
A 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 (l), somewhat satisfied (2), satisfied (3), and very satisfied (4). For each broker summary scores were computed by calculating a weighted average of the scores provided by each respondent. A portion of the survey results follow
Brokerage | Speed | Satisfaction |
Scottrade, Inc. | 3.6 | 3.3 |
Charles Schwab | 3.2 | 3.4 |
Fidelity Brokerage Services | 3.7 | 3.8 |
TD Ameritrade | 2.7 | 2.5 |
E*Trade Financial | 3.8 | 3.3 |
Vanguard Brokerage Services | 3.2 | 3.6 |
USAA Brokerage Services | 3.8 | 3.9 |
Thinkorswim | 2.7 | 2.9 |
Wells Fargo Investments | 2.9 | 2.4 |
Interactive Brokers | 3.9 | 3.4 |
Zecco.com | 3.6 | 3.1 |
b. What does the scatter diagram developed in part (a) indicate
about the relationship between the two variables? The scatter
diagram indicates a _______ linear relationship between speed of
execution rating and overall satisfaction rating for electronic
trades.
c. Develop the least squares estimated regression equation. Enter
negative value as negative number.
Satisfaction = ____ + ____ speed?
(to 4 decimals)
d. Provide an interpretation for the slope of the estimated
regression equation (to 4 decimals).
The slope of the estimated regression line is approximately ______.
So, a one unit ________in the speed of execution rating will
increase the overall satisfaction rating by
approximately_______points.
e. Suppose Thinkorswim developed new software to increase their speed of execution rating. If the new software is able to increase their speed of execution rating from the current value of 2.7 to the average speed of execution rating for the other 10 brokerage firms that were surveyed, what value would you predict for the overall satisfaction rating? ____________ (to 3 decimals)
(a) Scatter Diagram:
I have computed all the values by R-STUDIO.
CODE & OUTPUTS:
X_speed <- c(3.6, 3.2, 3.7, 2.7, 3.8, 3.2, 3.8, 2.7, 2.9,
3.9, 3.6)
Y_satisfaction <- c(3.3, 3.4, 3.8, 2.5, 3.3, 3.6, 3.9, 2.9, 2.4,
3.4, 3.1)
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(3.6, 3.2, 3.7, 2.7, 3.8, 3.2, 3.8, 2.9, 3.9,
3.6)
summary(X_new_10)
Pearson's product-moment correlation
data: X_speed and Y_satisfaction
t = 3.2053, df = 9, p-value = 0.01074
alternative hypothesis: true correlation is not equal to 0
95 percent confidence interval:
0.2317061 0.9248987
sample estimates:
cor
0.7301009
Call:
lm(formula = Y_satisfaction ~ X_speed)
Residuals:
Min 1Q Median 3Q Max
-0.4680 -0.2582 -0.1134 0.3034 0.4982
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 0.60845 0.8265 0.736 0.4804
X_speed 0.77916 0.2431 3.205 0.0107 *
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 0.3474 on 9 degrees of freedom
Multiple R-squared: 0.533, Adjusted R-squared:
0.4812
F-statistic: 10.27 on 1 and 9 DF, p-value: 0.01074
summary(X_new_10)
Min. 1st Qu. Median Mean 3rd Qu. Max.
2.700 3.200 3.600 3.440 3.775 3.900
regression_model$coefficients
(Intercept) X_speed
0.6084595 0.7791630
~~~~~~~~~~~Thanks~~~~~~~~~~