Research Question 1: Is there a linear relationship between the quality of food
ID: 3222989 • Letter: R
Question
Research Question 1: Is there a linear relationship between the quality of food ratings (Food) and the average cost of dinner for two (Cost). [Cost is the response variable.]
Is the sample size large enough? Explain.
Report relevant sample statistics.
Draw and interpret appropriate graphs for (a) each variable separately and (b) the relationship between the two variables.
Write the null and alternative hypotheses.
Write decision rules for both the critical and p-value approaches.
Use R to obtain the test statistic and p-value.
What is the appropriate statistical decision (Reject or FTR Ho)?
Organize the df, sums of squares, etc. into a summary ANOVA table.
Compute and interpret the coefficient of determination.
Research Question 2: Is there a linear relationship between the ambiance ratings (Ambiance) and the average cost of dinner for two (Cost). [Cost is the response variable.] Report relevant sample statistics.
Is the sample size large enough? Explain.
Draw and interpret appropriate graphs for (a) each variable separately and (b) the relationship between the two variables.
Write the null and alternative hypotheses.
Write decision rules for both the critical and p-value approaches.
Use R to obtain the test statistic and p-value.
What is the appropriate statistical decision (Reject or FTR Ho)?
Organize the df, sums of squares, etc. into a summary ANOVA table.
Compute and interpret the coefficient of determination.
Location Food Ambiance Service Cost City 22 14 19 33 City 20 15 20 26 City 23 19 21 43 City 19 18 18 32 City 24 16 18 44 City 22 22 21 44 City 22 20 20 50 City 20 19 19 42 City 21 17 19 44 City 20 18 18 36 City 23 22 24 61 City 20 19 20 50 City 21 19 21 51 City 24 19 21 50 City 25 23 23 76 City 22 21 21 53 City 23 15 22 44 City 26 22 24 77 City 21 23 21 57 City 24 15 19 43 City 21 15 19 29 City 23 16 16 34 City 25 21 26 77 City 22 20 21 50 City 26 25 24 74 City 23 21 21 56 City 22 19 17 67 City 26 20 23 57 City 26 23 25 66 City 24 23 24 80 City 22 23 23 68 City 24 16 23 42 City 20 17 19 48 City 25 19 23 60 City 23 20 21 35 City 21 19 22 45 City 20 16 18 32 City 23 15 18 25 City 26 24 24 74 City 21 18 18 43 City 22 16 19 39 City 19 23 21 55 City 24 19 21 65 City 23 16 20 35 City 24 26 22 61 City 21 17 18 37 City 21 17 19 54 City 23 19 22 41 City 23 19 21 33 City 23 14 19 27 Suburban 24 20 22 47 Suburban 22 18 22 48 Suburban 18 13 18 35 Suburban 22 23 20 59 Suburban 22 18 24 44 Suburban 23 25 24 51 Suburban 20 12 18 37 Suburban 19 18 19 36 Suburban 22 19 21 43 Suburban 27 21 27 52 Suburban 19 14 18 34 Suburban 22 11 19 38 Suburban 24 22 24 51 Suburban 19 15 19 34 Suburban 21 23 21 51 Suburban 21 19 21 34 Suburban 23 19 23 51 Suburban 23 20 22 56 Suburban 21 13 19 26 Suburban 24 19 22 34 Suburban 20 18 20 34 Suburban 24 22 24 44 Suburban 23 17 22 40 Suburban 23 16 21 31 Suburban 23 18 22 54 Suburban 19 12 22 41 Suburban 22 17 21 50 Suburban 26 27 24 71 Suburban 22 21 23 60 Suburban 19 15 17 37 Suburban 21 12 20 27 Suburban 26 18 22 34 Suburban 22 25 21 48 Suburban 21 21 21 39 Suburban 20 20 20 44 Suburban 22 18 22 41 Suburban 23 20 19 37 Suburban 24 21 23 47 Suburban 23 27 22 67 Suburban 24 24 22 68 Suburban 26 17 24 49 Suburban 22 22 19 29 Suburban 24 18 22 33 Suburban 20 19 20 39 Suburban 26 19 23 39 Suburban 22 15 21 28 Suburban 18 20 18 46 Suburban 26 27 25 70 Suburban 25 26 23 60 Suburban 22 25 22 52Explanation / Answer
Is there a linear relationship between the quality of food ratings (Food) and the average cost of dinner for two (Cost). [Cost is the response variable.]
Answer:
For checking the linear relationship or association exists between the two variables we have to find the sample correlation coefficient. The correlation coefficient between the two variables quality of food ratings and the average cost of dinner for two is given as 0.489538, this means there is a considerable positive linear relationship or association exists between the two variables quality of food ratings and the average cost of dinner for two. We have to check whether the given correlation coefficient is significant or not.
Is the sample size large enough? Explain.
Answer:
The given sample size is 100, so it is adequate sample size for using the different tests of hypothesis or regression analysis because as per thumb rule, we need the sample size at least 30 for making inference.
Report relevant sample statistics
Answer:
The relevant sample statistics includes the descriptive statistics which are given as below:
Descriptive Summary
Food
Mean
22.42
Median
22
Mode
22
Minimum
18
Maximum
27
Range
9
Variance
4.3067
Standard Deviation
2.0753
Coeff. of Variation
9.26%
Skewness
0.0569
Kurtosis
-0.5085
Count
100
Standard Error
0.2075
Descriptive Summary
Cost
Mean
46.85
Median
44
Mode
44
Minimum
25
Maximum
80
Range
55
Variance
180.2500
Standard Deviation
13.4257
Coeff. of Variation
28.66%
Skewness
0.5957
Kurtosis
-0.3276
Count
100
Standard Error
1.3426
Draw and interpret appropriate graphs for (a) each variable separately and (b) the relationship between the two variables.
Answer:
Here, we have to draw the scatter plot for the given two variables. The scatter plot is given as below:
From the above scatter plot it is observed that there is no any significant relationship exists between the given two variables food and cost.
Write the null and alternative hypotheses.
Answer:
The null and alternative hypothesis for this test is given as below:
Null hypothesis: H0: There is no any significant linear relationship exists between the dependent variable cost and independent variable food.
Alternative hypothesis: Ha: There is a significant linear relationship exists between the dependent variable cost and independent variable food.
The regression analysis for more reference is given as below:
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.489538448
R Square
0.239647892
Adjusted R Square
0.231889197
Standard Error
11.76656161
Observations
100
ANOVA
df
SS
MS
F
P-value
Regression
1
4276.456727
4276.456727
30.88765483
0
Residual
98
13568.29327
138.4519722
Total
99
17844.75
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Intercept
-24.15508021
12.83013008
-1.88268397
0.062709399
-49.61605515
1.305894719
Food
3.167041936
0.569851042
5.557666311
2.35673E-07
2.036191119
4.297892754
Descriptive Summary
Food
Mean
22.42
Median
22
Mode
22
Minimum
18
Maximum
27
Range
9
Variance
4.3067
Standard Deviation
2.0753
Coeff. of Variation
9.26%
Skewness
0.0569
Kurtosis
-0.5085
Count
100
Standard Error
0.2075
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