Interpret the slope and the intercept. What is the Pearson correlation coefficient (r) and interpret? RestaurantWebsite Hits (x) Weekly revenue $ (y)John's Café1,21312,113Buccan1,49011,409New City Diner1,36514,579Black Pearl1,45511,605Saratoga1,26912,308Burnt Toast1,63212,320University Seat1,32313,225Jimmy'sMaroon and Orange1,86513,6521,59013,893Burger Place1,87813,896 SUMMARY OUTPUTY = 1.67+ 10,382.37xRegression StatisticsMultiple RR SquareAdjusted R SquareStandard Error0.3571112390.1275284370.0184694921078.961437Observations10ANOVAdfSSMSSignificance FRegression11361311.7381361311.7381.1693532940.311050553Residual8.9313262.2621164157.783Total10674574t StatUpper 95%15808.53709CoefficientsStandard ErrorP-valueLower 95%Lower 95.0%Upper 95.0%10382.37282InterceptWebsite Hits (x)2353.0592114.4122871050.0022495264956.2085444956.20854415808.537091.6695140481,5438930281.0813664010.311050553-1.890709665.229737756-1.890709665.229737756RESIDUAL OUTPUTPROBABILITY OUTPUTPredicted Weekly revenue $ (y)Weekly revenue $ (y)11409ObservationResidualsStandard ResidualsPercentile1.12407.49336-294.4933559-0.289498181512869.94875-1460.948747-1.4361682411511605312661.259491917.7405091.8852119342512113412811.51576-1206.515755-1.186050923351230812500.98614-192.9861426-0.1897127264512320613107.01974-787.0197419-0.773670375513225712591.1399633.86009890.62310861651365213496.01652155.98348490.1533377047513893913036.90015856.09984810.84157874585138961013517.7202378.27980230.3718634489514579

The regression analysis is a statistical procedure that allow us to find the linear association…

Answered: nterpret the slope and the intercept.…

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nterpret the slope and the intercept. What is the Pearson correlation coefficient (r) and interpret?

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Author:Amos Gilat

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Concept explainers

Correlation

Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.

Linear Correlation

A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.

Regression Analysis

Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.

Question

Interpret the slope and the intercept. What is the Pearson correlation coefficient (r) and interpret?

Restaurant
Website Hits (x) Weekly revenue $ (y)
John's Café
1,213
12,113
Buccan
1,490
11,409
New City Diner
1,365
14,579
Black Pearl
1,455
11,605
Saratoga
1,269
12,308
Burnt Toast
1,632
12,320
University Seat
1,323
13,225
Jimmy's
Maroon and Orange
1,865
13,652
1,590
13,893
Burger Place
1,878
13,896

SUMMARY OUTPUT
Y = 1.67+ 10,382.37x
Regression Statistics
Multiple R
R Square
Adjusted R Square
Standard Error
0.357111239
0.127528437
0.018469492
1078.961437
Observations
10
ANOVA
df
SS
MS
Significance F
Regression
1
1361311.738
1361311.738
1.169353294
0.311050553
Residual
8.
9313262.262
1164157.783
Total
10674574
t Stat
Upper 95%
15808.53709
Coefficients
Standard Error
P-value
Lower 95%
Lower 95.0%
Upper 95.0%
10382.37282
Intercept
Website Hits (x)
2353.059211
4.412287105
0.002249526
4956.208544
4956.208544
15808.53709
1.669514048
1,543893028
1.081366401
0.311050553
-1.89070966
5.229737756
-1.89070966
5.229737756
RESIDUAL OUTPUT
PROBABILITY OUTPUT
Predicted Weekly revenue $ (y)
Weekly revenue $ (y)
11409
Observation
Residuals
Standard Residuals
Percentile
1.
12407.49336
-294.4933559
-0.289498181
5
12869.94875
-1460.948747
-1.436168241
15
11605
3
12661.25949
1917.740509
1.885211934
25
12113
4
12811.51576
-1206.515755
-1.186050923
35
12308
12500.98614
-192.9861426
-0.189712726
45
12320
6
13107.01974
-787.0197419
-0.77367037
55
13225
7
12591.1399
633.8600989
0.62310861
65
13652
13496.01652
155.9834849
0.153337704
75
13893
9
13036.90015
856.0998481
0.841578745
85
13896
10
13517.7202
378.2798023
0.371863448
95
14579

Definition Definition Statistical measure used to assess the strength and direction of relationships between two variables. Correlation coefficients range between -1 and 1. A coefficient value of 0 indicates that there is no relationship between the variables, whereas a -1 or 1 indicates that there is a perfect negative or positive correlation.

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